If |A|=|B| and |A+B|=√3|A-B|, find the angle between them in degrees.

Question

G1 Physics · Accepted Answer

For equal magnitude a: |A+B|²=2a²(1+cosθ), |A−B|²=2a²(1−cosθ). Ratio of squares is 3, so (1+c)/(1−c)=3, giving c=1/2 and θ=60°.