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Question

If a,b,c are unit vectors, then ab2+bc2+ca2 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 D 9
a+b+c0
a+b+c2=a2+b2+c2+2(a.b+b.c+c+a)0
a2+b2+c2+2(a.b+b.c+c+a)0
Since a,b,c are unit vectors
we have 3+2(a.b+b.c+c+a)0
a.b+b.c+c.a32 .............(1)
ab2+bc2+ca2
=2a2+2b2+2c22(a.b+b.c+c.a)
=2+2+22(a.b+b.c+c.a)
=62(a.b+b.c+c.a)
=62(32)=6+3=9 using (1)

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