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Let vec(A), vec(B) and vec(C), be unit v...

Let `vec(A), vec(B)` and `vec(C)`, be unit vectors. Suppose that `vec(A).vec(B)=vec(A).vec(C)=0` and the angle between `vec(B)` and `vec(C)` is `pi/6` then

A

`vec(A)=(vec(B)xxvec(C))`

B

`vec(A)=2(vec(B)xxvec(C))`

C

`vec(A)=2(vec(C)xxvec(B))`

D

`|vec(B)xxvec(C)|=sqrt(3)/2`

Text Solution

Verified by Experts

The correct Answer is:
B, C
As `vec(A) bot vec(B)` and `vec(A) bot vec(C)` so `vec(A)=+-((vec(B)xxvec(C)))/(|vec(B)xxvec(C)|)` But `|vec(B)xxvec(C)|=BC sin 30^(@)=1/2`
So `vec(A)=+-2(vec(B)xxvec(C))rArr vec(A)=2(vec(B)xxvec(C))` and `vec(A)=-2(vec(B)xxvec(C))=2(vec(C)xxvec(B))`
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