A vector describes a movement from one point to another. 3D vectors exist in the xyz plane. The 3D coordinates for any point have three values.

Part of

We saw previously how to represent 2D vectors on the \(xy\) plane.

Now, we will extend this to look at 3D vectors using the \(xyz\) plane.

3D coordinates are used, for example, by air traffic controllers to find the location of a plane by its height as well as its grid reference.

The vector OP has initial point at the origin O (0, 0, 0) and terminal point at P (2, 3, 5). We can draw the vector OP as follows:

Remember that 3D coordinates take the form \((x,y,z)\)