Maths

Vectors

A vector is a set of instructions for moving from one point to another in three dimensions. A line which has both magnitude and direction can represent this vector.

Given two points A(1, 3, 8) and B(3, 6, 5) then the directed line segment represents a set of instructions for moving from A to B. In order to get from A to B, you need to increase the x-co-ordinates by 2, increase the y-co-ordinates by 3 and *decrease* the z-co-ordinates by 3.

We write .

is just one way to represent the vector

Given P(1, 4, 8) and Q(-3, 1, -4), find . To do this, think yourself into the position of point P. How many units in each direction would you have to travel to reach point Q? A quick way to do this is to subtract the values of the co-ordinates of P from the co-ordinates of Q.

Take care to subtract the right set of co-ordinates. You'd get a very different answer if you subtracted Q from P instead.

It follows that you can also work out the co-ordinates of a point if you have the co-ordinates of another point and the vector that connects them.

Given P(1, 4, 10) and is a representative of vector , find Q.

means so if P=(1, 4, 10) then Q=(3, 5, 9)

The position vector is the vector from the origin to P. If P = (3, 4, -2), say, then . is called the position vector of P. We write .

If then the length or magnitude of , written as , is given by

Links

BBC © 2014 The BBC is not responsible for the content of external sites. Read more.

**This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.**