If `veca,vecb and vecc` are non coplanar and unit vectors such that `vecaxx(vecbxxvecc)=(vecb+vecc)/sqrt92)` then the angle between `vea and vecb` is (A) `(3pi)/4` (B) `pi/4` (C) `pi/2` (D) `pi`

Explanation

`vecaxx(vecbxxvecc)=(vecbxxvecc)/sqrt2`
`(veca .vecc)vecb-(veca.vecb)vecc=1/sqrt2vecb+1/sqrt2vecc`
Since `vecb and vecc` are non-collinear, comparing coefficients of `vecc` on both sides of (i) , we get
`-veca.vecb=1/sqrt2or veca.vecb=-1/sqrt2`
`(1) (1) cos theta=-1/sqrt2`
Where `theta` is the angle between `veca and vecb` .therefore,
`cos theta=-1/sqrt2or cos theta=cos135^(@)or theta=135^(@)=3pi//4`