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Question

If a,b and c are unit vectors then, |ab|2+|bc|2+|ca|2 can take the value of

A
3
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B
5
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C
12
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D
8
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Solution

The correct options are
A 3
B 5
D 8
|ab|2+|bc|2+|ca|2=a2+b2+b2+c2+c2+a22[a.b+b.c+c.a]
=62[a.b+b.c+c.a](1)
Since a,b & c are unit vectors
|a+b+c|0
a2+b2+c2+2[a.b+b.c+ca]0
3+2[a.b+b.c+c.a]0[a.b+b.c+c.a]32(2)
By (1) & (2),
|ab|2+|bc|2+|ca|262329

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