Let →a,→b,→c be unit vectors and α,β,γ be the angles between →b,→c;→c,→a;→a,→b respectively.If ∣∣∣→a+→b+→c∣∣∣=1, the cosα+cosβ+cosγ=
A
0
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B
−1
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C
2
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D
32
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Solution
The correct option is B−1 ∣∣∣→a+→b+→c∣∣∣=1 ⇒∣∣∣→a+→b+→c∣∣∣2=1 ⇒∣∣→a∣∣2+∣∣∣→b∣∣∣2+∣∣→c∣∣2+2.→a.→b+2.→b.→c+2.→c.→a=1 since →a,→b,→c are unit vectors ⇒1+1+1+2cosα+2cosβ+2cosγ=1 ⇒2cosα+2cosβ+2cosγ=−2 ⇒cosα+cosβ+cosγ=−1