If |A+B|=|A|=|B|, then the angle between A and B in . . .

Question : If |A+B|=|A|=|B|, then the angle between A and B in degrees is 40n. Find n.

Doubt by Suhani 

Solution : 

|A+B|=|A|=|B| = x (Let)
Also,
R=A=B=x

θ = 40n°

Using 
R = √[A²+B²+2ABcosθ]
squaring both sides
R²=A²+B²+2ABcosθ
(x)²=(x)²+(x)²+2(x)(x)cos(40n°)

x²=x²+x²+2x²cos(40n°)

x²=2x²+2x²cos(40n°)

x²=2x²[1+cos(40n°)]

1/2=1+cos(40n°)

1/2-1=cos(40n°)

-1/2=cos(40n°)

cos(120°)=cos(40n°)
40n°=120°
n=120°/40°
n=3

Hence, the required value of n is 3.

Similar Questions : 

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

2.) Two equal forces have their resultant equal to either. What is the inclination between them?