Let `veca, vecb` and `vecc` be three unit vectors such that `vecaxx(vecbxxvecc)=(sqrt(3))/2(vecb+vecc)`. If `vecb` is not parallel to `vecc` , then the angle between `veca` and `vecb` is

Options

A. `(3pi)/4`
B. `(pi)/2`
C. `(2pi)/3`
D. `(5pi)/6`

Answer

D

Explanation

We have
`vecaxx(vecbxxvecc)=(sqrt(3))/2(vecb+vecc)`
`implies(veca.vecc)vecb-(veca.vecb)vecc=(sqrt(3))/2(vecb+vecc)`
`implies(veca.vecc-(sqrt(3))/2)vecb-(veca.vecb+(sqrt(3))/2)vecc=vec0`
`impliesveca.vecc-(sqrt(3))/2=0` and `veca.vecb+(sqrt(3))/2=0` [ `:' vecb` and `vecc` are not parallel vectors]
`implies cos theta_(1)=(sqrt(3))/2` and `cos theta_(2)=(sqrt(3))/2` where `theta_(1)` and `theta_(2)` are angles made by `veca` with `vecc` and `vecb` respectively.
`implies theta_(1)=(pi)/6` and `theta_(2)=(5pi)/6`