If given the angle the vector makes with the x or y axis and the magnitude of the vector, we can work out the vector equations using trigonometry (SOHCAHTOA).

Examples of vectors in physics are force (requires a magnitude of the force and the direction), velocity (the speed is the magnitude and you are given the direction). For calculations, it is often easier to resolve these vectors into their x and y components.

Given any 2 points A and B, they have position vectors a and b which are just vectors from the origin to those points. We can also have the position vector from A to B, which is equal to b − a. Note that the position vector from B to A would be a − b. The distance between A and B is just the length of any position vector between them.

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