question_answer 5)

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:

(a) True. The magnitude of a vector is a pure number and has no direction. (b) False. Each component of a vector is also a vector. (c) False. The displacement depends only on the end points while the path length depends on the actual path. The two quantities are equal only if the direction of motion of the object does not change. In all other cases, path length is greater than the magnitude of displacement. (d) True. This is because the total path length is either greater than or equal to the magnitude of displacement over the same interval of time. (e) True. This is because the resultant of two vectors will not lie in the plane of third vector and hence cannot cancel its effect to give null vector.