How to do Vector Addition to get Net Force

One basic skill we use over and over in physics and engineering is adding vectors to find the total, or resultant or net, vector.  Vectors are those quantities with BOTH magnitude and DIRECTION, such as forces.  Obviously, gravity has a direction of 'down' and is therefore a vector.

The easiest problem is when there are two vectors on the same line, called colinear vectors.  These we just add, if in the same direction, or subtract, if in opposite directions.  The trickier problems are when forces are pulling in multiple dimensions.  This is where the rules for right triangles are needed.  We can use sine, cosine, and tangent to figure out how much of each individual force is in the x and y directions.  We can also use these functions to determine the direction of the net force, and therefore the direction the object will actually start moving.  Remember Chief SOH-CAH-TOA for the definitions of these trig functions!

Check out this example with three force vectors.  Keep in mind to use a table of x and y components in all your problems to keep things organized - it will help.