How can i find the magnitude AND direction of F2 relative to F1 in the problem below?

Two horses pull horizontally on ropes attached to a stump. The two forces F1 = 1210 N and F2 that they apply to the stump are such that the net (resultant) force R has a magnitude equal to that of F1 and makes an angle of 90 degrees with F1. |||The net force is the vector sum of the forces, so





F = F1 + F2


F is perpendicular to F1 so the dot pproduct must be zero





F鈥1 = 0 = |F1|^2 + F1鈥2


or


F1鈥2 = - |F1|^2 = |F1||F2|Cos[ang]


or


Cos[ang] = -|F1|/|F2|





The magnitude of the resultant force is |F1|, so





F鈥 = |F1|^2 = |F1|^2 + |F2|^2 + 2F1鈥2





substitute for F1鈥2





|F1|^2 = |F1|^2 + |F2|^2 - 2|F1|^2


or


|F2| = Sqrt[2] |F1| This gives the magnitude of F2





Substitute this into the previous expression for Cos[ang]





Cos[ang] = -|F1|/|F2| = -1/Sqrt[2]





You can substitute to get the magnitude and angleween F1 and F2 that defines F2