Question

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. `-4` b. `-1//3` c. `1` d. `2`
A. `-1`
B. `-1//3`
C. `1`
D. `2`

Answer 1

Correct Answer - B::C
We have , `veca = 2phati+hatj`
on rotaion, let `vecb` be the vector with components (`p+1`) and 1 so that `vecb= (p+1)hati+hatj`.
Now, `|veca|= |vecb| or a^(2)= b^(2)`
`rArr 4p^(2) +1 = (p+1)^(2) +1`
or `4p^(2) = (p+1)^(2)`
or `2p = pm (p+1)`
`rArr 3p = -1 or p =1 `
`therefore p =-1//3 or p =1 `