# Position Vectors

A position vector is any vector that is placed extending from the origin. Position vectors are often denoted by , for example, to identify the vector that points from the origin to a point .

Let and be the position vectors that point from the origin to the points and respectively. We can then find the vector that points from to :

It is easy to visualise going from to by thinking of it as going backwards along , then forwards along .

There are a variety of problems involving position vectors. Examples 1 and 2 illustrate just two ways in which position vectors can be put into context.

## Vectors and Trigonometry

By now you will be very familiar with Pythagoras and SOHCAHTOA. This allows you to find angles and missing lengths in right-angled triangles. You may also have recently learned about non-right angled triangles. That is to say, you may have learned about the cosine rule, the sine rule and perhaps even how to find the area of a non-right angled triangle.

It is entirely possible that trigonometry may be used in the context of vectors. Examples 3 and 4 illustrate just two ways in which vectors can be using in a trigonometric setting.