Question
Read each statement below carefully and state with reasons, if 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 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.
Solution
(a)True, because magnitude is a pure number.
(b) False, each component of a vector is always a vector, not a scalar.
(c) False, total path length can also be more than the magnitude of displacement vector of a particle. e.g. when a particle follows the arc of circle, the length of path is greater than magnitude of the displacement.
This statement is true only if the particle is moving in a straight line.
(d) True, because the total path length is either greater than or equal to the magnitude of the displacement vector.
(e) True, as the three vectors cannot be represented by the three sides of a triangle taken in the same order.
