Three forces act on an object. a 3 n force acts due east and a 8 n force acts due north. if the net force on the object is zero, what is the magnitude of the third force?"

The third force C is in the opposite direction of the sum of the first two forces, A+B, but the magnitude is the same as A+B

Since A & B are at right angles we can just use Pythagoras and trig:

A+B magnitude = sqrt (6^2 + 3^2) = 6.71

A+B angle = arctan (6/3) deg north of east = 63.4 deg (first quadrant)

So C magnitude = 6.71 (same as A+B)

[C angle = 63.4 deg south of west (third quadrant) = - 180+63.4 deg polar = - 116.6 deg