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Let overset(to)(A),overset(to)(B)" and ...

Let `overset(to)(A),overset(to)(B)" and " overset(to)(C )` be unit vectors . If `overset(to)(A).overset(to)(B) = overset(to)(A).overset(to)(C ) =0` and that the angle between `overset(to)(B) " and " overset(to)(C )" is " pi//6.`
Then `overset(to)(A) =+-2 (overset(to)(B)xxoverset(to)(C ))`

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The correct Answer is:
1
Given `vec(A)". " vec(B) = vec(A) ". " vec(C ) =0`
`rArr vec(A) ` is perpendicular to both `vec(B) " and " vec( C )`
`rArr vec(A) = lambda (vec(B) xx vec( C))`
`|vec(A)|=|lambda||vec(B) xx vec(C )| " where " vec(A),vec(B),vec(C )` are unit vectors
`rArr |lambda|= (1)/(1. sin 30^(@)) rArr |lambda|=2 rArr lambda =+-2`
`:. vec(A) =+- 2 (vec(beta) xx vec(C ))`
Hence given statement is true .
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