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