let `veca , vecb and vecc` be three vectors having magnitudes 1, 1 and 2, respectively, if `vecaxx(vecaxxvecc)+vecb=vec0, ` then the acute angle between `veca and vecc` is _______

Options

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

Answer

B

Explanation

`veca xx (veca xx vecc)-vecb=0`
`rArr (veca.vecc)veca-(veca.veca)vecc-vecb=0`
`rArr (veca.vecc)veca-vecc=vecb`
`rArr |vecc-(veca.vecc)veca|^(2)=|vecb|^(2)`
If `theta` is the angle between `veca` and `vecc`, then `4+(2costheta)^(2)-2(2costheta)^(2)=1`
`rArr 4cos^(2)theta=3 rArr cos^(2)theta=3//4`
`rArr costheta=sqrt(3)//2 [therefore theta` is acute]
`rArr theta=pi//6`