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A vector has components p and 1 with res...

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

A

Both the statements are true, and Statement 2 is the correct explanation for Statement 1.

B

Both the statements are true, but Statement 2 is not the correct explanation for Statement 1.

C

Statement 1 is true and Statement 2 is false.

D

Statement 1 is false and Statement 2 is true.

Text Solution

Verified by Experts

The correct Answer is:
A
`sqrt((p+2)^(2)+1)= sqrt(p^(2)+1)`
or `p^(2)+4 +4p +1 = p^(2)+1`
or `4p=-4`
or `p=-1`
Hence, a is the correct option.
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