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Let hat(a) , hat(b) " and " hat( c) be ...

Let `hat(a) , hat(b) " and " hat( c)` be three unit vectors such that `hat(a) xx (hat(b) xx hat( c)) = (sqrt(3))/(2)( hat(b) +hat(c )).` If `hat(b)` is not parallel to `hat( c)` then the angle between `hat(a) " and " hat(b)` is

A

`(3pi)/(4)`

B

`(pi)/(2)`

C

`(2pi)/(3)`

D

`(5pi)/(6)`

Text Solution

Verified by Experts

The correct Answer is:
D
Given `|hat(a)| = |hat(b)| =|hat(c )| =1`
`" and " hat(a) xx (hat(b) xx hat(c )) hat(c ) = (sqrt(3))/(2) hat(b) + (sqrt(3))/(2) hat(c )`
On comparing we get
`hat(a) ". " hat(b) = - (sqrt(3))/(2)rArr |hat(a)| |hat(b)| cos 0 =- (sqrt(3))/(2)`
`rArr cos 0 =- (sqrt(3))/(2) [ :' |hat(a) | =|hat(b)| =1]`
`rArr cos 0 = cos (pi- (pi)/(6)) rArr 0 = (5pi)/(6)`
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