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Question

If a and b are two unit vectors inclined at an angle θ, such that a +b <1, then
(a) θ<π3

(b) θ>2π3

(c) π3<θ<2π3

(d) 2π3<θ<π

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Solution

(d) 2π3<θ<π

We have a +b <1a 2+b 2+2a ×b cosθ<112+12+2×1×1× cosθ<12+2 cosθ<121+ cosθ<12×2cos2θ2<12cosθ2<1cosθ2<12π3<θ2<2π32π3<θ<4π3But here θ cannot be more than π.2π3<θ<π

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