Question

Assertion :A vector has components $p$ and $1$ with respect to a rectangular Cartesian system. The axes are rotated through an angle $\alpha$ 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
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

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,
$\sqrt{(p+2{)}^2+1}=\sqrt{p^2+1}$
or $p^2+4+4p+1=p^2+1$
or $4p=-4$
or $p=-1$
The Reason is the correct explanation.
Hence, $A$ is the correct option.