Scalar and Vector Quantities

Scalar Quantities

The scalar quantities (or sometimes known as scalars) are those quantities which have magnitude only such as length, mass, time, distance, volume, density, temperature, speed, energy work etc.

Vector Quantities

The vector quantities (or sometimes known as vectors) are those quantities which have both magnitude and direction such as force, displacement, velocity, acceleration, momentum etc. Following are the important features of vector quantities.

Representation of a Vector

A vector is represented by a directed line as shown in Fig. 1. It may be noted that the length OA represents the magnitude of the vector OA. The direction of the vector OA is from O (i.e., starting point) to A (i.e., end point). It is also known as vector P.

Fig. 1 Vector OA

Unit Vector

A vector, whose magnitude is unity, is known as unit vector.

Equal Vectors

The vectors, which are parallel to each other and have same direction (i.e., same sense) and equal magnitude are known as equal vectors.

Like Vectors

The vectors, which are parallel to each other and have same sense but unequal magnitude, are known as like vectors.

Addition of Vectors

Consider two vectors PQ and RS, which are required to be added as shown in Fig. 2 (a). Take a point A and draw line AB parallel and equal in magnitude to the vector PQ to some convenient scale. Through B, draw BC parallel and equal to vector RS to the same scale. Join AC which will give the required sum of vectors PQ and RS as shown in Fig. 2 (b).

Fig. 2 Method of Addition of Vectors

This method of adding the two vectors is called the Triangle Law of Addition of Vectors. Similarly, if more than two vectors are to be added, the same may be done first by adding the two vectors, and then by adding the third vector to the resultant of the first two and so on. This method of adding more than two vectors is called Polygon Law of Addition of Vectors.

Subtraction of Vectors

Consider two vectors PQ and RS in which the vector RS is required to be subtracted as shown in Fig. 3 (a). Take a point A, and draw line AB parallel and equal in magnitude to the vector PQ to some convenient scale. Through B, draw BC parallel and equal to the vector RS, but in opposite direction, to that of the vector RS to the same scale. Join AC, which will give the resultant when the vector PQ is subtracted from vector RS as shown in Fig. 3 (b).

Fig. 3 Method of Subtraction of Vectors