Two vectors both equal in magnitude, have their . . .

Question :  Two vectors both equal in magnitude, have their resultant equal in magnitude of the either. Find the angle between the two vectors.

Doubt by Ankit 

Solution : 

A = Magnitude of first vector.
B = Magnitude of second vector.
R = Magnitude of the resultant vector. 
A=B=R (Given)

A=B=R = x (Let)

We know, 
R=√(A²+B²+2ABcosθ)
R²=A²+B²+2ABcosθ
x²=x²+x²+2(x)(x)cosθ [∵A=B=R = x]
x²=2x²+2x²cosθ
x²=2x²(1+cosθ)
x²/2x²=1+cosθ
1/2=1+cosθ
(1/2)-1=cosθ
-1/2=cosθ
cosθ=-1/2
cosθ=cos120°
θ=120°

Hence, the required angle between the two vectors in 120°