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# Representation of vectors in Cartesian coordinates.

The most commonly used method to represent a vector is with Cartesian coordinates. The units can be anything, but to start with, we could just consider the ``displacement vector'' which describes the difference in position of two points in space. You just plonk your vector on top of an x-y grid and read off the numbers on the x and y axes. Here's what I mean.

So this (two dimensional) vector, call it is represented by a pair of numbers. The first one is the x component of the vector, , which you get by reading it off this figure. You can see that it's 3. The y component, , can also be read of and is 5.5. So you could write this vector as (3,5.5). If this vector was three dimensional (which is more difficult to draw), then it would be represented by three numbers.

But why did I place the grid the way that I did? Wouldn't I have been equally justified in plonking the vector on top of a grid going at some other angle, liked so?