Question

For two non-zero vectors a and b, vector R=a+b such that |ā|=|b|=|R|, then angle made by a with b is
90°
60°
120°
30°​

Answer 1

Answer:

120

Explanation:

R^2 = A^2 + B^2 + 2AB cosθ

But R=A=B

Hence, A^2 = A^2 + A^2 + 2A^2 cosθ

⟹ cosθ = -1/2

Hence, θ = 120  

Answer 2

Given :  For two non-zero vectors a and b, vector  R=a+b such that |ā|=|b|=|R|,

To Find : angle made by a with b  

90°

60°

120°

30°​

Solution:

|ā|=|b|=|R|  = k

θ is the angle between a  and b

|R| = √ |ā|² +  |b|² + 2 |ā||b|Cosθ

=> k = √k² + k² + 2k²Cosθ

=> k² = 2k² + 2k²Cosθ

=> 1 = 2 + 2Cosθ

=> 2Cosθ = -1

=> Cosθ = -1/2

=> θ = 120°

Hence  angle made by a with b is 120°

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