A 2.44 kg object is subjected to three forces that give it an acceleration vector a = -(8.00 m/s2)i hat + (6.00 m/s2)j hat. If two of the three forces are vector F1 = (30.7 N)i hat + (17.0 N)j hat and vector F2 = -(12.0 N)i hat + (8.00 N)j hat, find the third force.

Answer 1

Treat the i and j components separately
Also, noting that F = ma,

(30.7-12.0+x) = -8.00*2.44
(17.0+8.00+y) = 6.00*2.44

That will give you the third force, xi+yj