When two vectors vector A and vector B are drawn from a common point, the angle between them is phi.

Question

If vector A and vector B have the same magnitude, for which value of phi will their vector sum have the same magnitude as vector A or vector B?

Answer 1

When the triangle of forces is an equilateral triangle, i.e. when φ=120°. So Acos(φ/2)+Bcos(φ/2)=A/2+B/2=A=B