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A force acting on a body has a magnitude and a direction. Vectors describe the direction of a force along a two or three dimensional axis. If more than one force act on a body, the resultant direction of the force is obtained through vector addition.
For instant, consider two vectors a and b. The resultant vector r is obtained by the following operation:
a = <3,0,-9>
b = <-2,-5,10>
a + b = r = <3+(-2),1+(-5),-9+10> = <1,-4,1>
The resultant vector will now have the coordinates <1,-4,1> in a three dimensional Cartesian coordinate system.