Let `veca, vecb` and `vecc` be three having magnitude 1,1 and 2 respectively such that `vecaxx(vecaxxvecc)+vecb=vec0`, then the acute angle between `veca` and `vecc` is

Options

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

Answer

C

Explanation

Let `theta` b the angle between `veca` and `vecc`.Then
`vecaxx(vecaxxvecc)+vecb=vec0`
`implies(veca.vecc)veca-(veca.veca)vecc+vecb=vec0`
`implies(2cos theta)veca-vecc+vecb=0 [ :' veca.vecc=cos theta` and `|veca|=|vecb|=1,|vecc|=2]`
`implies(2cos theta)veca-vecc=-vecb`
`implies|(2cos theta)veca-vecc|^(2)=|vecb|^(2)`
`implies 4cos^(2)theta|veca|^(2)+|vecc|^(2)-4cos theta (veca.vecc)=|vecb|^(2)`
`implies 4cos^(2) theta+4-4cos theta (2cos theta)=1`
`implies 4 cos^(2)theta=3impliescos theta=(sqrt(3))/2impliestheta=(pi)/6`