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
π≥θ>2π3
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D
π3<θ<2π3
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Solution
The correct option is Dπ3<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 ∴−1≤cosθ<−12 ⇒π≥θ>2π3