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The vector vec a has the components 2p ...

The vector ` vec a` has the components `2p` and 1 w.r.t. a rectangular Cartesian system. This system is rotated through a certain angel about the origin in the counterclockwise sense. If, with respect to a new system, ` vec a` has components `(p+1)a n d1` , then `p` is equal to

A

p=0

B

p=1 or `p=-(1)/(3)`

C

p=-1 or `p=(1)/(3)`

D

p=1 or `p=-1`

Text Solution

Verified by Experts

The correct Answer is:
B
We have, `a=2p hati+hatj`
Or rotation, let b be the vector with components (p+1) and 1 so that,
`b=(p+1)hati+hatj`
Now, `|a|=|b|impliesa^(2)=b^(2)`
`implies4p^(2)+1=(p+1)^(2)+1implies4p^(2)=(p+1)^(2)`
`implies2p=+-(p+1)implies3p=-1` or p=1
`therefore p=-(1)/(3)` or p=1.
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