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.

(A) True: The magnitude of a vector is a real number representing its length. Hence,it is a scalar.
$(b)$ False: Each component of a vector is a vector quantity directed along the coordinate axes.
$(c)$ False: Total path length is the actual distance traveled,which is a scalar,while the magnitude of displacement is the shortest distance between the initial and final positions. Total path length is greater than or equal to the magnitude of displacement.
$(d)$ True: Since total path length is always greater than or equal to the magnitude of displacement,dividing both by the same time interval leads to the average speed being greater than or equal to the magnitude of average velocity.
$(e)$ True: Three vectors not lying in a plane cannot form a closed triangle,which is a necessary condition for their sum to be a null vector.