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Question

Let |a|=1,b=2, |c|=3, and a(b+c), b(c+a) and c(a+b), then a+b+c is

A
6
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B
6
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C
14
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D
None of these
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Solution

The correct option is C 6
Now a is perpendicular to (b+c)
Hence a.(b+c)=0
a.b+a.c=0
Similarly b.c+b.a=0
a.c+b.c=0
Adding all the three gives us
2(a.b+b.c+c.a)=0
Now |a+b+c|
=a.a+b.b+c.c+2(a.b+b.c+c.a)
=a2+b2+c2
=1+2+3
=6

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