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Question

If a,b,c are unit vectors, then |ab|2+|bc|2+|ca|2 does not exceed :

A
4
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B
9
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C
8
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D
6
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Solution

The correct option is A 9
E=|ab|2+|bc|2+|ca|2
2(1+1+1)2ab(|a|=|b|=|c|=1)
=62|a||b|...(i)
Again (a+b+c)20
(1+1+1)+2ab032ab or 3E6 or 9EE9 (by(1))
Hence E does not exceed 9.

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