If →a,→b,→c are unit vectors, then |→a−→b|2+|→b−→c|2+|→c−→a|2 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 A 9 E=|→a−→b|2+|→b−→c|2+|→c−→a|2 2(1+1+1)−2∑→a⋅→b(∵|→a|=|→b|=|→c|=1) =6−2∑|→a|⋅|→b|...(i) Again (→a+→b+→c)2≥0 ∴(1+1+1)+2∑→a⋅→b≥0⇒3≥−2∑→a⋅→b or 3≥E−6 or 9≥E∴E≥9 (by(1)) Hence E does not exceed 9.