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Question

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+c2=1
a2+b2+c2+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

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