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 the 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, because magnitude is a pure number and directionless. (b) False, vector is sum of its components.(Note: Magnitude of each component is a scalar) (c) False, because total path length is greater than or equal to magnitude of displacement vector, whenever direction of motion changes. (d) True, because the total path length is either greater than or equal to the magnitude of the displacement vector. (e) True, as they can not be represented by the three sides of a triangle taken in the same order.
