Position Vectors

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

Let $\overrightarrow{OA}$ and $\overrightarrow{OB}$ be the position vectors that point from the origin to the points $A$ and $B$ respectively. We can then find the vector that points from $A$ to $B$ :

$\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}$

It is easy to visualise going from $A$ to $B$ by thinking of it as going backwards along $\overrightarrow{OA}$ , then forwards along $\overrightarrow{OB}$ .

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 SOH CAH TOA. 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