How do I begin...? Well, adding vectors is basically to determine the closest distance between two points (displacement) Using Mr. Chung's analogy, basically let one point represent A.Y. Jackson, and the second point represent the Pacific Mall. Although utilizing this analogy requires the location of A.Y. Jackson to vary, it is very useful.
Basically, adding straight vectors usually produce a diagonal line to represent the closest distance between the two points. These two vectors can therefore be calculated using the pythagorean theorem. After the determining the length of the hypoteneuse, you then have to determine the orientation and the direction of the hypoteneuse using sin/cos/tan in which the angle has to be measured as the part that is outside of the angle at the origin. (in this case it's 90-feta if the orientation is NE and it's feta if the orientation is SW)
For vectors that begin as a diagonal line, all you need to do is calculate the distance on the two sides (that create the triangle) using sin/cos. Apply the previous logics and voila!
Now you know how to calculate vectors!
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