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Question

Let a,b and c be three vectors such that a+b+c=0, and |a|=10,|b|=6 and |c|=14.

Fund the value of a.b+b.c+c.a.

A
332
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B
166
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C
0
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D
166
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Solution

The correct option is B 166
a+b+c=0
(a+b+c).(a+b+c)=0

|a|2+|b|2+|c|2+2(a.b)+2(b.c)+2(c.a)=0

100+36+196+2(a.b+b.c+c.a)=0

a.b+b.c+c.a=166

So, the answer is option (B)

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