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Question

Let A,B and C be unit vectors. Suppose that AB=AC=0 and that the angle between B and C is π6 then A=

A
±2(B×C)
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B
±(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 A ±2(B×C)
Since, AB=0,AC=0
Hence, (B+C)A=0
So A is perpendicular to (B+C)A is a unit vector perpendicular to the plane of vectors B and C.
A=B×CB×C
B×C=BCsinπ6=1×1×12=12
A=B×CB×C=±2(B×C)

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