A vector has magnitude and direction. Does it have a location in space ? Can it vary with time ? Will two equal vectors $a$ and $b$ at different locations in space necessarily have identical physical effects ? Give examples in support of your answer.

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Solution

(i) A vector in general has no definite location in space because a vector remains unaffected whenever it is displaced anywhere in space provided its magnitude and direction do not change. However, a position vector has a definite location in space.
(ii) A vector can vary with time as example the velocity vector of an accelerated particle varies with time.
(iii) Two equal vectors at different locations in space do not necessarily have same physical effects. For example, two equal forces acting at two different points on a body which can cause the rotation of a body about an axis will not produce equal turning effect.

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A vector has magnitude and direction. Does it have a location in space ? Can it vary with time ? Will two equal vectors a and b at different locations in space necessarily have identical physical effects ? Give examples in support of your answer.

A vector has magnitude and direction. Does it have a location in space ? Can it vary with time ? Will two equal vectors $a$ and $b$ at different locations in space necessarily have identical physical effects ? Give examples in support of your answer.