If →a,→b,→c are the 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 B9 Given expression =2(1+1+1)−2∑(→a.→b) =6−2∑(→a.→b).......(i) But (→a+→b+→c)≥0 ∴(1+1+1)+2∑→a.→b≥0 ∴3≥−2∑→a.→b.......(ii) From Eqs.(i) and (ii), Given expression≤6+3=9