Adding Vectors

Firstly: What is a vector?
A vector is a quantity that is specified in both direction and magnitude. Vectors possess both a head and a tail, the tail being the start of the arrow and the head being the end of the arrow. Vectors are also written with direction, which can be indicated with and angle, or just a simple [N], [E], [S] or [W] for the simpler vectors.

The notation for the vector on the left would be 20m [N30W].

In order to add vectors, you must look at both the magnitude and the direction. The picture on the left shows how to add vectors that are going in the same or opposite directions. In order to add vectors that are not going in the same or opposite directions, we must use the Pythagorean Theorem. For example, if you have two arrows, one of them being 11km [N] and the other one being 11km [E], the resultant (R) can be found by using the formula a^2 + b^2 = c^2.

But wait, we're not done yet. Vectors have to have both magnitude and direction. We've already figured out magnitude, but now we have to figure out direction. This is explained by the next two pictures: