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 magnitude of a vector is always a scalar - True, The magnitude of a vector is a number. Hence, it is a scalar

(b) each component of a vector is always a scalar- False, Each component of a vector is also a vector.

(c) the total path length is always equal to the magnitude of the displacement vector of a particle.- False, Total path length is a scalar quantity, whereas displacement is a vector quantity. Hence, the total path length is always greater than the magnitude of displacement. It becomes equal to the magnitude of displacement only when a particle is moving in a straight line. 

(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, - True, It is because of the fact that the total path length is always greater than or equal to the magnitude of displacement of a particle. 

(e) Three vectors not lying in a plane can never add up to give a null vector. - True, Three vectors, which do not lie in a plane, cannot be represented by the sides of a triangle taken in the same order.