The vector ` vec a`has the components `2p`and 1 w.r.t. arectangular Cartesian system. This system is rotated through a certain angelabout the origin in the counterclockwise sense. If, with respect to a newsystem, ` vec a`has components `(p+1)a n d1`, then `p`is equal toa. `-4`b. `-1//3`c. `1`d. `2`A. `-1`B. `-1//3`C. `1`D. `2`

The vector ` vec a`has the components `2p`and 1 w.r.t. arectangular Ca

1.	The vector ` vec a`has the components `2p`and 1 w.r.t. arectangular Cartesian system. This system is rotated through a certain angelabout the origin in the counterclockwise sense. If, with respect to a newsystem, ` vec a`has components `(p+1)a n d1`, then `p`is equal toa. `-4`b. `-1//3`c. `1`d. `2`A. `-1`B. `-1//3`C. `1`D. `2`
Answer» 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 `

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