Question

Read each statement below carefully and state with reasons, if it is true or false : (a) The magnitude of a vector is always a scalar, (b) each component of a vector is always a scalar, (c) the total path length is always equal to the magnitude of the displacement vector of a particle. (d) the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time, (e) Three vectors not lying in a plane can never add up to give a null vector.

Answer 1

(a)

The given statement is true. For example, even though displacement is a vector quantity, but its magnitude is scalar quantity and it may be equal to the distance.

(b)

The given statement is false, since the components of a vector is always a vector. For example, the projectile motion has both horizontal and vertical components of velocity, and they both are vector quantities.

(c)

The given statement is false. The total path length may or may not be equal to the magnitude of the displacement vector. For example, the distance covered by an object in one complete revolution around a circular path is equal to the circumference of the circular path. But the displacement of the object is zero.

(d)

When the velocity is negative, the average speed comes out to be positive. In this case average velocity is greater than average speed.

When the velocity is positive, the average speed comes out to be positive. In this case the average velocity is equal to the average speed.

Or simply, we can say the path length is always greater than or equal to the displacement.

Hence, the given statement is true.

(e)

The resultant of the three vectors that are not lying in the same plane can be added upto given a null vector. It is because; they can be added only if they are in the same plane.

Hence, the given statement is true.