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Question

Assertion :A vector has components p and 1 with respect to a rectangular Cartesian system. The axes are rotated through an angle α about the origin in the anticlockwise sense.

If the vector has components p+2 and 1 with respect to the new system, then p=1
Reason: Magnitude of the original vector and the new vector remains the same.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
The magnitude of the vector would remain the same in both the reference frames.
Hence,
(p+2)2+1=p2+1
or p2+4+4p+1=p2+1
or 4p=4
or p=1
The Reason is the correct explanation.
Hence, A is the correct option.

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