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Question

Let a,b,c be three unit vectors such that a+b+c=1 and ab. If c makes angle α,β with a,b respectively then cosα+cosβ is equal to

A
32
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B
1
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C
1
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D
None of these
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Solution

The correct option is C 1
Consider
¯¯¯a=i
¯¯b=j
¯¯c=i
Now
¯¯¯a+¯¯b+¯¯c
=ii+j
=j
Hence |¯¯¯a+¯¯b+¯¯c|=1

If a.c=|a||c|cosα
i.(i)=cos(α)
cosα=1
Now
b.c=|b||c|cosβ
j.(i)=cos(β)
cosβ=0
Hence
cosα+cosβ=1

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