{"id":197984,"date":"2022-06-20T13:30:00","date_gmt":"2022-06-20T08:00:00","guid":{"rendered":"https:\/\/www.aakash.ac.in\/blog\/?post_type=web-story&#038;p=197984"},"modified":"2022-09-03T18:12:56","modified_gmt":"2022-09-03T12:42:56","slug":"maths-how-to-find-dot-product-of-two-vectors-cbse-12th-notes","status":"publish","type":"web-story","link":"https:\/\/www.aakash.ac.in\/blog\/web-stories\/maths-how-to-find-dot-product-of-two-vectors-cbse-12th-notes\/","title":{"rendered":"How to Find Dot Product of Two Vectors | CBSE 12TH Maths Notes"},"content":{"rendered":"<p><html amp=\"\" lang=\"en\"><head><meta charSet=\"utf-8\"\/><meta name=\"viewport\" content=\"width=device-width,minimum-scale=1,initial-scale=1\"\/><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0.js\"><\/script><script async=\"\" src=\"https:\/\/cdn.ampproject.org\/v0\/amp-story-1.0.js\" custom-element=\"amp-story\"><\/script><link 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style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6349206349206349% 0.6349206349206349% 0.6349206349206349% 0.6349206349206349% \/ 2.197802197802198% 2.197802197802198% 2.197802197802198% 2.197802197802198%\" id=\"el-8d19cf2a-e493-45fb-9f83-a4b9f1bef8dd\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.22619047619047575% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.404531em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #edf6f6\">How to Find Dot Product of Two Vectors | CBSE 12TH Maths Notes<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:8.98058%;top:8.09061%;width:80.09709%;height:70.87379%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-80042526-db4b-4d33-aef7-84a9cd6059d9\">\n<div style=\"position:absolute;width:100%;height:133.94216%;left:0%;top:-16.97108%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-18.png\" alt=\"Dot product (18)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-18.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-18-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-18-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-18-150x267.png 150w\" sizes=\"(min-width: 1024px) 36vh, 80vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:0;width:14.07767%;height:9.38511%;opacity:1\">\n<div 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1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#fbfbf9\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-e92604a0-839e-4c05-9635-3caaf91395d3\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44.jpg\" alt=\"44\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/44-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.8932%;top:5.66343%;width:76.45631%;height:13.59223%;opacity:1\">\n<div id=\"anim-65da4f22-e9fd-452e-be65-d240d35469d1\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-115.55555%, 0px, 0)\">\n<div id=\"anim-07ad1b2a-2913-46e7-82cf-79ff79669d65\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-b9f75f48-627a-4641-a820-fd642a66b04d\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6349206349206349% 0.6349206349206349% 0.6349206349206349% 0.6349206349206349% \/ 2.380952380952381% 2.380952380952381% 2.380952380952381% 2.380952380952381%\" id=\"el-f132b5e0-e9cf-46e5-8ecb-4865c4fb24d1\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.20809523809523808% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.372168em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">The scalar product of two vectors is known as the <\/span><span style=\"font-weight: 700; color: #edf6f6\">dot product of two vectors<\/span><span style=\"color: #edf6f6\">.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:10.92233%;top:27.6699%;width:77.6699%;height:69.25566%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-80916e2b-af85-4611-a715-75345f3664cd\">\n<div style=\"position:absolute;width:131.1259%;height:174.28987%;left:-14.07249%;top:-50.69688%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-12.png\" alt=\"Dot product (12)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-12.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-12-576x1024.png 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style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6349206349206349% 0.6349206349206349% 0.6349206349206349% 0.6349206349206349% \/ 2.380952380952381% 2.380952380952381% 2.380952380952381% 2.380952380952381%\" id=\"el-3a52164b-1c62-4b8d-91f9-b7b3217c15c9\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.20809523809523808% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.372168em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">There are two methods to find the dot product of two vectors:<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:26.86084%;width:76.45631%;height:9.06149%;opacity:1\">\n<div id=\"anim-f6e6d04d-b48f-4e77-a4f6-0aaf7f325074\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-115.2381%, 0px, 0)\">\n<div id=\"anim-0a9f1617-bbcb-4c7c-91a4-b08cfef9d974\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-e859fe3f-9189-4702-acae-1d44aa4a1135\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6349206349206349% 0.6349206349206349% 0.6349206349206349% 0.6349206349206349% \/ 3.571428571428571% 3.571428571428571% 3.571428571428571% 3.571428571428571%\" id=\"el-f23d5c16-d754-47f5-9754-d0f53c1f9672\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.20809523809523808% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.372168em;line-height:1.2;text-align:left;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">\u2013 Dot Product Geometry<\/span><br \/>\n<span style=\"color: #edf6f6\">\u2013 Dot Product Algebra<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:2.18447%;top:39.80583%;width:95.63107%;height:49.51456%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-f702b3e3-89db-4c50-ae4e-62ba061fc81b\">\n<div style=\"position:absolute;width:100%;height:228.90343%;left:0%;top:-93.54495%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-11.png\" alt=\"Dot product (11)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-11.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-11-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-11-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-11-150x267.png 150w\" sizes=\"(min-width: 1024px) 43vh, 96vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"85c9614c-29fd-4e82-b5a1-4c45f92c4ab3\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-572d1c30-c1f7-4d5f-b93c-5fe18eeaee4b\",\"keyframes\":[{\"offset\":0,\"transform\":\"translate3d(0, -707.778%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.29,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.45,\"transform\":\"translate3d(0, -199.0271736%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.61,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.71,\"transform\":\"translate3d(0, -67.6635768%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.8,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.85,\"transform\":\"translate3d(0, -25.409230200000003%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":0.92,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"},{\"offset\":0.96,\"transform\":\"translate3d(0, -11.0413368%, 0)\",\"easing\":\"cubic-bezier(.5, 0, 1, 1)\"},{\"offset\":1,\"transform\":\"translate3d(0, 0%, 0)\",\"easing\":\"cubic-bezier(0, 0, .5, 1)\"}],\"delay\":0,\"duration\":1300,\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#1a92cb\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-811c91a8-080c-406e-a0ac-6460df646fbe\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Classroom-Artboard-6.jpg\" alt=\"Classroom-Artboard 6\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Classroom-Artboard-6.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Classroom-Artboard-6-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Classroom-Artboard-6-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Classroom-Artboard-6-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:69.41748%;width:76.94175%;height:12.94498%;opacity:1\">\n<div id=\"anim-572d1c30-c1f7-4d5f-b93c-5fe18eeaee4b\" class=\"animation-wrapper\" 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style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.13308359621451105% 0;font-family:&quot;Roboto&quot;,&quot;Helvetica Neue&quot;,&quot;Helvetica&quot;,sans-serif;font-size:0.485437em;line-height:1.2;text-align:center;padding:1.2618296529968454% 2.5236593059936907%;color:#000000\"><span><span style=\"font-weight: 700; color: #fff\">Click Here To Attend Free Trail Class<\/span><\/span><\/p>\n<p><\/a><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-page-outlink layout=\"nodisplay\" cta-image=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/08\/Aakash-Icon-Blue-PNG.png\"><a href=\"https:\/\/byjus-aakash.onelink.me\/GieR\/aakashwebstories\" rel=\"\">Download Aakash App<\/a><\/amp-story-page-outlink><\/amp-story-page><amp-story-page id=\"cf8413e8-8638-4f52-ab50-24cfd17449fa\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-ffb7f3e3-a28d-46ec-b993-a03e6f6f4059\",\"keyframes\":{\"transform\":[\"translate3d(-115.2381%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-a6b2f37b-4dee-44ca-b19e-aab56a668576\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-3f06128c-b836-4b87-9bc3-bab0bf481844\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#262626\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-cc302e49-ae4f-4241-8ad9-bd5867ce56b7\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/15.jpg\" alt=\"15\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/15.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/15-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/15-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/15-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:6.95793%;width:76.45631%;height:22.49191%;opacity:1\">\n<div id=\"anim-ffb7f3e3-a28d-46ec-b993-a03e6f6f4059\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-115.2381%, 0px, 0)\">\n<div id=\"anim-a6b2f37b-4dee-44ca-b19e-aab56a668576\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-3f06128c-b836-4b87-9bc3-bab0bf481844\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6349206349206349% 0.6349206349206349% 0.6349206349206349% 0.6349206349206349% \/ 1.4388489208633095% 1.4388489208633095% 1.4388489208633095% 1.4388489208633095%\" id=\"el-fca7fa23-9bd7-42ac-a7f5-7a5a8a198e26\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.20809523809523808% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.372168em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"font-weight: 700; color: #edf6f6\">Dot Product Geometry<\/span><span style=\"color: #edf6f6\"> is the dot product of two non-zero vectors denoted by a.b and is calculated using the formula:<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:6.79612%;top:36.8932%;width:86.40777%;height:38.83495%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-0e5a519a-43fe-4b20-90e8-7b8521682c23\">\n<div style=\"position:absolute;width:100%;height:263.70372%;left:0%;top:-46.88572%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-5.png\" alt=\"Dot product (5)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-5.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-5-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-5-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-5-150x267.png 150w\" sizes=\"(min-width: 1024px) 39vh, 86vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"f6716bb2-7d68-4a26-a208-354bd367ed9f\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-5414d542-d548-4989-aef7-686cbcdf53c3\",\"keyframes\":{\"transform\":[\"translate3d(-115.14196%, 0px, 0)\",\"translate3d(0px, 0px, 0)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-f48d0589-ef97-4ce4-b689-4c20e59b51c3\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-3c2b328e-832e-42e3-8f16-120ffaaffe4d\",\"keyframes\":{\"transform\":[\"scale(0.15)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(0.4, 0.4, 0.0, 1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#12191b\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-b16d29e8-ec4d-4990-a5e1-26487661d642\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/48.jpg\" alt=\"48\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/48.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/48-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/48-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/48-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:11.65049%;width:76.94175%;height:13.1068%;opacity:1\">\n<div id=\"anim-5414d542-d548-4989-aef7-686cbcdf53c3\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:translate3d(-115.14196%, 0px, 0)\">\n<div id=\"anim-f48d0589-ef97-4ce4-b689-4c20e59b51c3\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-3c2b328e-832e-42e3-8f16-120ffaaffe4d\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.15)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6309148264984227% 0.6309148264984227% 0.6309148264984227% 0.6309148264984227% \/ 2.4691358024691357% 2.4691358024691357% 2.4691358024691357% 2.4691358024691357%\" id=\"el-eea4e601-32c7-41af-a313-09b7405a871b\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:0.19779179810725517% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.2;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">According to the <\/span><span style=\"font-weight: 700; color: #edf6f6\">Dot Product Algebra<\/span><span style=\"color: #edf6f6\">, the dot product of the two products<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:9.95146%;top:17.96117%;width:80.09709%;height:94.82201%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-97185f43-555a-4cd2-8ba8-b9d1c7d509f9\">\n<div style=\"position:absolute;width:100%;height:100.11377%;left:0%;top:-0.05688%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-6.png\" alt=\"Dot product (6)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-6.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-6-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-6-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-6-150x267.png 150w\" sizes=\"(min-width: 1024px) 36vh, 80vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"43946efa-4942-4387-b717-5a141e0a7118\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-ca9b77a4-b50f-4952-bb64-f2e9683e8286\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-6bb53fda-0f83-416b-aa87-ca12058be391\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#1b2b3a\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-7a69b55e-f222-43e0-aeef-f2bb2f78207e\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/43.jpg\" alt=\"43\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/43.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/43-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/43-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/43-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.40777%;top:11.48867%;width:77.18447%;height:9.54693%;opacity:1\">\n<div id=\"anim-ca9b77a4-b50f-4952-bb64-f2e9683e8286\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-6bb53fda-0f83-416b-aa87-ca12058be391\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.628930817610063% 0.628930817610063% 0.628930817610063% 0.628930817610063% \/ 3.389830508474576% 3.389830508474576% 3.389830508474576% 3.389830508474576%\" id=\"el-ac3d2033-e30c-4985-a14f-73d9cb09da37\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.49465408805031463% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.355987em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">To understand dot product geometry<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:-0.32362%;width:80.09709%;height:94.82201%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-e1771903-30e4-43c0-9f75-d37652724ffb\">\n<div style=\"position:absolute;width:100%;height:100.11377%;left:0%;top:-0.05688%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-7.png\" alt=\"Dot product (7)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-7.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-7-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-7-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-7-150x267.png 150w\" sizes=\"(min-width: 1024px) 36vh, 80vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:4.12621%;top:47.57282%;width:91.74757%;height:42.0712%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-d6b7442c-d2a4-442d-929f-070002287031\">\n<div style=\"position:absolute;width:100%;height:258.46151%;left:0%;top:-55.19869%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-9.png\" alt=\"Dot product (9)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-9.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-9-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-9-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-9-150x267.png 150w\" sizes=\"(min-width: 1024px) 41vh, 92vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><amp-story-page id=\"9d5d5b65-826d-4db7-81c2-9d3314847315\" auto-advance-after=\"9s\"><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-21db6a46-de6a-46bb-b251-3936a5a131c5\",\"keyframes\":{\"opacity\":[0,1]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"both\"}]<\/script><\/amp-story-animation><amp-story-animation layout=\"nodisplay\" trigger=\"visibility\"><script type=\"application\/json\">[{\"selector\":\"#anim-e17aa6e9-51d9-402a-ba0e-65c6a1c23997\",\"keyframes\":{\"transform\":[\"scale(0.3333333333333333)\",\"scale(1)\"]},\"delay\":0,\"duration\":1300,\"easing\":\"cubic-bezier(.3,0,.55,1)\",\"fill\":\"forwards\"}]<\/script><\/amp-story-animation><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\" style=\"background-color:#3f3f41\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:0;top:-9.25926%;width:100%;height:118.51852%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-422138dc-231d-4ecb-acf0-d433806c3c54\">\n<div style=\"position:absolute;width:100%;height:100%;left:0%;top:0%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/35.jpg\" alt=\"35\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/35.jpg 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/35-576x1024.jpg 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/35-169x300.jpg 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/05\/35-150x267.jpg 150w\" sizes=\"(min-width: 1024px) 45vh, 100vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<div class=\"element-overlay-area\" style=\"background-image:radial-gradient(ellipse 67% 67%, rgba(0,0,0,0) 0%, rgba(0,0,0,0.7) 100%)\"><\/div>\n<\/div>\n<\/div>\n<div class=\"page-background-overlay-area\" style=\"background-image:radial-gradient(ellipse 67% 67%, rgba(0,0,0,0) 0%, rgba(0,0,0,0.7) 100%)\"><\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><amp-story-grid-layer template=\"vertical\" aspect-ratio=\"412:618\" class=\"grid-layer\"><\/p>\n<div class=\"page-fullbleed-area\">\n<div class=\"page-safe-area\">\n<div style=\"position:absolute;pointer-events:none;left:11.65049%;top:6.31068%;width:76.69903%;height:20.22654%;opacity:1\">\n<div id=\"anim-21db6a46-de6a-46bb-b251-3936a5a131c5\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:0;--initial-transform:none\">\n<div id=\"anim-e17aa6e9-51d9-402a-ba0e-65c6a1c23997\" class=\"animation-wrapper\" style=\"width:100%;height:100%;display:block;position:absolute;top:0;left:0;--initial-opacity:1;--initial-transform:scale(0.3333333333333333)\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0;border-radius:0.6329113924050633% 0.6329113924050633% 0.6329113924050633% 0.6329113924050633% \/ 1.6% 1.6% 1.6% 1.6%\" id=\"el-c7af149a-66c6-4978-a28c-d3fa96749d88\">\n<p class=\"fill text-wrapper\" style=\"white-space:pre-wrap;overflow-wrap:break-word;word-break:break-word;margin:-0.520411392405063% 0;font-family:&quot;Merriweather&quot;,serif;font-size:0.372168em;line-height:1.4;text-align:center;padding:0;color:#000000\"><span><span style=\"color: #edf6f6\">To explain dot product algebra, let us consider two vectors [6, 2, -1] and&nbsp;<\/span><br \/>\n<span style=\"color: #edf6f6\">[5, -8, 2] as an example.<\/span><\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div style=\"position:absolute;pointer-events:none;left:5.58252%;top:37.70227%;width:88.59223%;height:38.99676%;opacity:1\">\n<div style=\"pointer-events:initial;width:100%;height:100%;display:block;position:absolute;top:0;left:0;z-index:0\" class=\"mask\" id=\"el-ef78c39d-072a-476d-ab6f-6a8497be1057\">\n<div style=\"position:absolute;width:100%;height:269.24852%;left:0%;top:-54.34014%\" data-leaf-element=\"true\"><amp-img layout=\"fill\" src=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-8.png\" alt=\"Dot product (8)\" srcSet=\"https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-8.png 720w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-8-576x1024.png 576w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-8-169x300.png 169w,https:\/\/d20x1nptavktw0.cloudfront.net\/wordpress_media\/2022\/06\/Dot-product-8-150x267.png 150w\" sizes=\"(min-width: 1024px) 40vh, 89vw\" disable-inline-width=\"true\"><\/amp-img><\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><\/amp-story-grid-layer><\/amp-story-page><\/amp-story><\/body><\/html><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dot Product Geometry is the dot product of two non-zero vectors denoted by a.b and is calculated using the formula:<\/p>\n","protected":false},"author":1,"featured_media":0,"template":"","meta":{"web_stories_publisher_logo":224645,"web_stories_poster":[],"web_stories_products":[],"footnotes":""},"web_story_category":[2144,2352],"web_story_tag":[],"class_list":["post-197984","web-story","type-web-story","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>How to Find Dot Product of Two Vectors | CBSE 12TH Maths Notes - Aakash Blog<\/title>\n<meta name=\"description\" content=\"Dot Product Geometry is the dot product of two non-zero vectors denoted by a.b and is 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