Have you heard two terms Distance and Displacement? Both are used for quantifying length traveled by some object. Distance can be represented by magnitude only (say 5 km); Displacement cannot, it needs a direction also.
Any physical quantity can be divided into three parts:
1. Scalar quantities
2. Vector quantities
3. Tensor quantities
Quantities with magnitude as well as direction but don't obey the laws of vector addition or subtraction are tensor quantities. For example- stress, strain, electric current,etc.
Tensors are generalization of scalar and vector, scalar is zero order tensors, vector is first order tensor.
For the representation of vector quantities we use arrows, the length of the arrow represents the magnitude of vector quantities and arrow head represents the direction of the vector.
Let's consider an arrow as shown in figure above is representing a physical quantity having the length 2 units and is headed toward the east. So the magnitude of the quantity is 2 units and the direction is toward the east.
Symbolically, Vector is denoted by a right arrow over the letters representing the tail and head of the vector respectively.
In Rectangular notation, the vector is located in a rectangular coordinate system, as shown in above figure .
The rectangular notation for vector is
In the polar notation, we denote the vector magnitude by r,
Where r ≥ 0, and its angle θ with the positive x- axis as shown in the figure.
The Polar notation for vector is
Question 1. Which of the following quantities is scalar ?
(a) Displacement (b) Acceleration (c) Temperature (d) Force
Answer: To define Temperature only magnitude is needed. So, temperature is a scalar quantity. Hence option (c) is correct.
Question 2. Which of the following quantities is vector ?
(a) Speed (b) Velocity (c) Mass (d) Distance
Answer: To define Velocity magnitude and direction are needed.so, velocity is a vector quantity. Hence option (b) is correct.
Question 3. What is the magnitude of the quantity represented by the vector AB shown in figure below?
(a) 3 units (b) 4 units (c) 5 units (d) 6 units
Answer: The magnitude of the vector will be 5 units. Hence option (c) is correct.
Question 4. What is the direction of the quantity represented by the vector shown in figure below?
(a) East (b) North (c) North-East (d) North-South
Answer: Option (c) is correct.
Question 1. What is the scalar quantity ?
Answer: The quantity which is described only by its magnitude is called scalar quantity .
Question 2. What is vector quantity?
Answer: The quantity which is described by both its magnitude and direction is called vector quantity.
Question 3. Speed is scalar quantity or vector quantity?
Answer: speed is described by magnitude only for ex. 5 m/s, so scalar quantity.
Question 4. Force is scalar quantity or vector quantity?
Answer: Force is described by both magnitude as well as direction ,so vector quantity.
|Physical World||Units and Measurements|
|Motion in a Plane||Laws of Motion||Work Energy and Power|
|Gravitation||Mechanical Properties of Solids|
|Mechanical Properties in Liquids||Thermal Properties of Matter||Thermodynamics|