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If vec(A) and vec(B) are two non-zero ve...

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 `:`

A

`37^(@)`

B

`53^(@)`

C

`cos^(-1)(-3//4)`

D

`cos^(-1)(-4//3)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(A^(2)+B^(2)+2AB cos theta)=(1)/(4)(A^(2)+B^(2)-2ABcos theta)`
`rArr 3A^(2)+3B^(2)+10ABcos theta=0`
or `12B^(2)+3B^(2)+10(2B)(B) cos theta=0`
`15B^(2)+20B^(2)cos theta=0`
`cos theta=-(3)/(4)`
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