Chapter 2 Physics and Mathematics relates physics and maths. The fields of mathematics and physics are closely connected. The fields of mathematics and physics are closely linked. Physicists use mathematics as a tool to answer questions. For instance, Newton invented Calculus to best describe motion.
In this chapter, various terms required to understand physics are discussed. The shortest angle between two vectors at which any of the vectors can be rotated about the other vector in such a way that both have the same direction is called the angle between two vectors. Thus, for example,
if the two vectors are assumed as a⃗ and b⃗ then the dot created is articulated as a⃗ .b⃗.
Considering that an angle θ separates these two vectors, the dot product of the two vectors can be given as
"A⃗ .b⃗ =|a⃗ ||b⃗ |cosθ"
In simple words, the magnitude of a vector is nothing but its length. Therefore, it is denoted as ∥a∥.
The scalar X-component of a vector can be expressed as a product of its magnitude with the cosine of its direction angle. Similarly, the scalar Y-component can be expressed as a product of its magnitude with the sine of its direction angle. The chapter further discusses resultant vectors.
The vector sum of two or more vectors is termed the 'resultant vector'. Simply put, it is the result of adding two or more vectors together. For example, if the displacement vectors A, B, and C are added together, the resultant will be a vector R. The tangent of an angle can be defined as the trigonometric ratio of the adjacent and opposite sides of a right angle triangle comprising the angle. Therefore, tan θ= y component / x component.