The vector `hat(i)+xhat(j)+3hat(k)` is rotated through an angle `theta` and doubled in magnitude then it becomes `4hat(i)+(4x-2)hat(j)+2hat(k)`. The value of x is

Options

A. `{-(2)/(3),2}`
B. `{(1)/(3),2}`
C. `{(2)/(3),0}`
D. `{2,7}`

Answer

A

Explanation

Since , `2|hat(i)+xhat(j)+3hat(k)|=(4hat(i)+(4x-2)hat(j)+2hat(k)|`
`rArr 2sqrt(1+x^2+9)=sqrt(4^2+(4x-2)^2)+2^2)`
`rArr 12x^2-16x-16=0`
`rArr (3x+2)(x-2)=0rArr x=2,-(2)/(3)`