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Question

If a,b c are unit vectors such that a+b+c=0,then the value of a.b+b.c+c.a is

(a) 1 (b) 3

(c) 32 (d) None of these

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Solution

(c)We have,a+b+c=0 and a2=1,b2=1,c2=1 (a+b+c)(a+b+c)=0a2+a.b+a.c+b.a+b2+b.c+c.a+c.b+c2=0 a2+b2+c2+2(a.b+b.c+c.a)=0 [a.b=b.a,b.c=c.b and c.a=a.c] 1+1+1+2(a.b+b.c+c.a)=0 a.b+b.c+c.a=32


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