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Question

If ab, and 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 B 9
ab2=a2+b22a.bbc2=b2+c22b.cca2=c2+a22c.aab2+bc2+ca2=2(a2+b2+c2a.bb.cc.a)=2(3a.bb.cc.a)=62(a.b+b.c+c.a)(a+b+c)0a2+b2+c2+2(a.b+b.c+c.a)0a.b+b.c+c.a322(a.b+b.c+c.a)3ab2+bc2+ca26+39OptionBiscorrect.

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