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Question

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

A
All are acture angles
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B
All are right angles
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C
At least one is obtuse angle
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D
Exactly one is obtuse angle
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Solution

The correct option is C At least one is obtuse angle
Since a+b+c=1(a+b+c).(a+b+c)=1
1+1+1+2(a.b+b.c+c.a)=1
(a.b+b.c+c.a)=1
cosθ1+cosθ2+cosθ3=1
So atleast one of these 3 values cosθ must be negative.
So atleast one is obtuse angle.

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