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Question: Assertion(A): A vector is not changed if it is slid parallel to itself.
Reason(R):Two parallel vectors of the same magnitude are said to be equal vectors.
(A) Both A and R are true and R is correct explanation of A
(B) Both A and R are true but R is not correct explanation of A
(C) A is true but R is false
(D) A is false but R is true

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Last updated date: 13th Jun 2024
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Answer
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Hint A vector only changes when it is rotated through an arbitrary angle, multiplied by an arbitrary scalar, or if it is cross multiplied by the unit vector. But not on sliding parallel to itself (it remains unchanged).

Complete step by step solution
Correct answer: Both A and R are true but R is not the correct explanation of A.
 Definition of vector: A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector and with an arrow indicating the direction. The direction of the vector is from its tail to its head.
A vector is defined by its magnitude and direction and if we slide it to a parallel position to itself, then none of the given parameters defining the vector will change. Let the magnitude of a displacement vector $\vec A$ directed towards the south be 10 metres. If we slide it parallel to itself, then the direction and magnitude will not change.
When the two vectors have equal magnitude and same direction then they are said to be equal vectors.
In the given question the reason given is a condition for parallel vectors of the same magnitude and is not the correct explanation for the assertion.

Option B is correct answer

Note Vector is defined by its direction and its magnitude but not by its position in space it means if a vector is displaced parallel to itself (without changing its magnitude and its direction) then it does not change , it remains equal.