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Question

If a,b, and c are unit vectors such that a+2b+2c=0, then |a×c| is equal to :

A
154
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B
14
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C
1516
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D
1516
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Solution

The correct option is A 154
a+2b+2c=0a+2c=2b(a+2c)(a+2c)=(2b)(2b)1+4ac+4=4ac=14
Let the angle between a and c be θ
cosθ=14sinθ=±154
Now,
|a×c|=|a||c|sinθ=154

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