The constant forces F1 = (8i + 12j) newtons and F2 = (4i - 4j) newtons act on a particle. No other forces act on the particle. Find the resultant force.
This is a standard vector problem using (i,j) notation. (i,j) notation is the same as the standard Cartesian coordinate system where the horizontal axis is labeled with i, and vertical is j.
So, we use the same rules we normally would to find the resultant. R will have two componants that are along the i and j axis which are the sums of the i and j componants of the two applied vectors:
R = ([8i+4i] + [12j-4j]) = (12i + 8j)n
This would be the same as a Cartesian vector that has Rx=12n, Ry=8n
Or that R = (144+64)^1/2 at Tan^-1(8/12) = 14.4 n at 33.7 deg