If the magnitude of resultant 2pi vectors (f1&f2) of equal magnitude is one third of magnitude of one of the force. Find the angle between the forces.

Let the force vectors be A and B.Then |A| =|B| ….......................(1) {Given}And also,|A +B| = |A|Squaring both sides,|A|^2 + |B|^2 + 2.A.B = |A|^2|B|^2 + 2A.B = 0..........................(2)Now Angle between the tqo vectors is:cos@ = A.B/|A|.|B| = A.B/|B|^2 (Given = |A| =|B|). From eqn. (2)A.B/|B|^2 = -1/2 = cos@@ = 120 degree.