1. y x z Forces => Vectors => 2D and 3D
Force System = 2 or more forces acting on a body (particle or mass)
Resultant =  forces in the system
R = F = F1 + F2 + F3
where R = Rxî + Ryĵ + Rzk
Let’s look at three random forces and find the resultant analytically and graphically. x z y

2. F1 = 2N 30 1st quadrant
F2 = 4N 150 2nd quadrant
F3 = 6N -45 = 6N 315 th quadrant
F1 = 2N 30
= 2 cos 30 î sin 30 ĵ
= î ĵ
F2 = 4N 150
= 4 cos 150 î sin 150 ĵ
= (-)3.464 î ĵ
F3 = 6N 315
= 6 cos 315 î sin 315 ĵ
= î + (-)4.243 ĵ

3. Add like terms of these forces to get the resultant,
R = F = F1 + F2 + F3
F1 = î ĵ
+ F2 = (-)3.464 î ĵ
+ F3 = î (-)4.243 ĵ
R = î (-)1.243 ĵ
R = Rx î Ry ĵ
Convert resultant to polar coordinates.
magnitude =  (2.511)² + (-1.243)² =  2.8 N
orientation = tan-1 (rise / run)
= tan-1 (-1.243/2.511) = 
 R = 2.8 N -26.3  2.8 N 334