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Question

If a,b and c are unit vectors, then the value of |ab|2+|bc|2+|ca|2 does not exceed

A
6
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B
8
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C
9
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D
16
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Solution

The correct option is C 9
|ab|2+|bc|2+|ca|2=2(|a|2+|b|2+|c|2)2(ab+bc+ca)=2×3+3[3+2(ab+bc+ca)][|a|=|b|=|c|=1]=9(|a+b+c|2)9
So, maximum value is 9.

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