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 A.
Let and 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:
It is easy to visualise going from A to B by thinking of it as going backwards along , then forwards along .
There are a variety of problems involving position vectors. The two examples directly below 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. The two examples directly below illustrate just two ways in which vectors can be using in a trigonometric setting.
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