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Question

If a and b are unit vectors and θ is the angle between them, then |a+b|<1, if

A
θ=π2
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B
θ<π3
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C
πθ>2π3
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D
π3<θ<2π3
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Solution

The correct option is D π3<θ<2π3
Given |a|=1 and |b|=1
|a+b|<1
|a+b|2<1
|a|2+|b|2+2|a||b|cosθ<1
1+1+2cosθ<1
cosθ<12
1cosθ<12
πθ>2π3

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