Explanation:
|F|= B/2
B/2 = √(A²+B²+2ABcosθ) ------(1)
Since the resultant of A and B is perpendicular to Vector A
tan90°= BSinθ/(A+BCosθ)
(A+BCosθ)=0
Cosθ=-A/B ----(2)
Using equation (1)
B/2 = √(A²+B²+2ABcosθ)
B/2 = √(A²+B²+2AB×-A/B)
B/2=√(A²+B²-2A²)
B/2=√(B²-A²)
B²/4=B²-A²
A²=B²-B²/4
A²=3B²/4
A=√3B/2
Using equation (2)
Cosθ=-A/B
Cosθ=-[√3B/2]/B
Cosθ=-√3/2
θ= cos^-1 (-√3/2)
θ= 150°
