Read each statement below carefully and state with reason, if it … - Vidyadip

Question

Read each statement below carefully and state with reason, 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) It is true, since the magnitude of a vector is always a number.
(b) It is wrong, since the component of every vector is also a vector.
(c) False, it is true only when the particle moves along a straight line in the same direction.
(d) True, because the total path length is equal to or greater than the displacement vector. Hence, the average speed is greater than or equal to the magnitude of average velocity.
(e) True, to get the zero vector the third vector should have same magnitude but opposite direction.

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