Let ` vec a , vec b"and" vec c` be there unit vectors such that ` vec axx( vec bxx vec c)=(sqrt(3))/2( vec b+ vec c)` . If ` vec b` is not parallel to ` vec c` , then the angle between ` vec a"and" vec b` is: (1) `(3pi)/4` (2) `pi/2` (3) `(2pi)/3` (4) `(5pi)/6`

Explanation

Let angle between `veca` and `vecb` is `theta`.

We are given,

`veca xx (vecb xx vecc) = sqrt3/2(vecb+vecc)`

`=>(veca*vecc)vecb - (veca*vecb)vecc = sqrt3/2(vecb+vecc)`


`=>veca*vecc = sqrt3/2 and veca*vecb = -sqrt3/2`

`=>|veca||vecb|costheta = -sqrt3/2`

`=>1*1*costheta = -sqrt3/2` ...(As a and b are unit vectors)

`=>theta = pi-pi/6`

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