The vector `hati+xhatj+3hatk` is rotated through an angle `theta` and doubled in magnitude, then it becomes `4hati+(4x-2)hatj+2hatk`. Then values of x are (A) `-2/3` (B) `1/3` (C) `2/3` (D) 2

Options

A. 1
B. `(-2)/(3)`
C. `2`
D. `(4)/(3)`

Answer

B, C

Explanation

let `alpha=hati+xhatj+3hatk`,
`beta=4hati+(4x-2)hatj+2hatk`
Given, `2|alpha|=|beta|`
`implies 2sqrt(10+x^(2))=sqrt(20+4(2x-1)^(2))`
`implies10+x^(2)=5+(4x^(2)-4x+1)`
`implies3x^(2)-4x-4=0`
`impliesx-2,-(2)/(3)`