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Q.

If a^,b^ and c^ are three unit vectors and a^+b^+ c^  is also a unit vector and θ1,θ2 and θ3  are angles between the vectors    a^,b^;b^,c^ and c^,a^   respectively, then among  θ1,θ2 and θ3

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a

all are acute angles

b

all are right angles

c

at lest one is obtuse angle

d

none of these

answer is C.

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Detailed Solution

|a→+b→+c→|2=1⇒ |a→|2+|b→|2+|c→|2+2|a→||b→|cos⁡θ1 +2|b→||c→|cos⁡θ2+2|c→∥a→|cos⁡θ3=1⇒ cos⁡θ1+cos⁡θ2+cos⁡θ3=−1Hence, one of θ1,θ2 and θ3 should be an obtuse angle.
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