Two non-zero vectors P and Q are such that P+Q=R . . .

Question : Two non-zero vectors P and Q are such that P+Q=R and |P|=|Q|=|R|. If angle between P and Q is n×30°, find the value of n.

Doubt by Suhani

Solution : 

P+Q=R (Given)

θ=n×30° (Given)

|P|=|Q|=|R|=x (Let)

We know, 
R²=P²+Q²+2PQcosθ
x²=x²+x²+2(x)(x)cosθ
x²=2x²+2x²cosθ
x²=2x²(1+cosθ)
x²/2x²=(1+csoθ)
1/2=1+csoθ
1/2-1=cosθ

-1/2=cosθ

cos120°=cosθ

cos120°=cos(n×30°)

120°=n×30°
120°/30°=n
4=n

n=4

Hence, n=4