Read each statement below carefully and state with reasons, with it is true or false :
(a) The magnitude of 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 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.

Explanation

a) True, magnitude of the veloicty of a body moving in a straight line may be equal to the speed of the body.
b)False, each component of a vector is always a vector, not scalar
c)False, total path length can be also be more than the magnitude of displacement vector of a particle.
d) True, because the total path length is either greater than or equal to the magntitude of the displacement vector.
e) True, this is because the resultant of two vectors will not be in the plane of third vector and hence, cannot cancel its effect to give null vector.