If `vec(A)` and `vec(B)` are two non`-`zero vectors such that `|vec(A)+vec(B)|=(|vec(A)-vec(B)|)/(2)` and `|vec(A)|=2|vec(B)|` then the angle between `vec(A)` and `vec(B)` is `:`

Options

A. `37^(@)`
B. `53^(@)`
C. `cos^(-1)(-3//4)`
D. `cos^(-1)(-4//3)`

Answer

C

Explanation

`(A_(2)+B_(2)+2AB cos theta)=(1)/(4)`
`(A_(2)+B_(2)-2AB cos theta)`
`rArr 3A_(2)+3B_(2)+10AB cos theta =0`
or `12B_(2)+3B_(2)+10(2B)(B)cos theta=0`
`15B_(2)+20B_(2) cos theta =0`
`cos theta=-(3)/(4)`.