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Question

Let A,B,C be unit vectors. Suppose A.B=A.C=0 and the angle between B and C is π6. Then A equals

A
±2(B×C)
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B
2(B×C)
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C
2(B×C)
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D
(B×C)
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Solution

The correct option is D ±2(B×C)
Since A.B=A.C=0
A is to the plane B and C
Also, B×C=|B||C|sinπ6ˆn=12ˆn
But A=ˆn, both being unit vectors to the plane of B and C
A=±2(B×C)

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