Vectors `veca, vecb, vecc` are three unit vectors and `vecc` is equally inclined to both `veca` and `vecb`. Let
`veca xx (vecb xx vecc) + vecb xx (vecc xx veca)`
`=(4+x^(2))vecb-(4xcos^(2)theta)veca`,
then `veca` and `vecb` are non-collinear vectors, `x gt 0`

Options

A. `x=2`
B. `theta=0^(@)`
C. `theta=x`
D. `x=4`

Answer

A, B, C

Explanation

`|veca|=|vecb|=|vecc|=1`
and `veca.vecc=vecb.vecc`………….(i)
`veca xx (vecb xx vecc) +vecb xx (vecc xx veca)`
`=(vecc. vecc)vecb-(veca.vecb)vecc+(veca.vecb)vecc-(vecb.vecc)veca`
`=(veca.vecc)vecb-(vecb.vecc)veca`
`rArr veca.vecc+x^(2)` and `vecb.vecc=4xcos^(2)theta`. ........(ii)
From (i) and (ii), `4+x^(2)=4xcos^(2)theta`
`rArr 4+x^(2)=4x-4sin^(2)theta`
`rArr (x-2)^(2)=-4xsin^(2)theta`
`rArr x=2` or `sintheta=0`.