In Chapter 8, we discussed vectors and their interpretation in 2D. As you might have guessed, all of the things we discussed there still hold in 3D space as well. All we need to do is to add one more coordinate to our vector, namely the z-coordinate.
The operations we looked at with vectors in 2D can be easily transferred to 3D space. We specify vectors in 3D with a statement like the following:
v = (x, y, z)
Addition in 3D is carried out as follows:
c = a + b = (a.x, a.y, b.z) + (b.x, b.y, b.z) = (a.x + b.x, a.y + b.y, a.z + b.z)
Subtraction works exactly the same way:
c = a - b = (a.x, a.y, b.z) - (b.x, b.y, b.z) = (a.x - b.x, a.y - b.y, a.z - b.z)
Multiplying a vector by a scalar works like this:
a' = a × scalar = (a.x × scalar, ...