I'm trying to understand the maths of moving points in a 3d space by making a game written in C#.

I'm looking at this wolfire blog series which explains some basic 3d maths. I've read the first two parts but am stuck on the 3rd. I know it's all really rudimentary stuff but I find Googling for help with equations really hard.

The one I'm struggling with is:

0*(0.66,0.75) + 2*(-0.75, 0.66) = (-1.5, 1.3)

How can anything multiplied by 0 not be 0?

So my question is how does this look in code:

x(a,b) + y(c,d)

I know it's basic stuff but I just can't see it.