How to calculate the normals(and normalize) of this quad?
Assuming the quad is planar. Create two vector from one vertex to two other vertices. The normal is the crossproduct of the two vectors. To normalize it, divide all components by it’s length.
It’s very basic maths that one should understand when doing 3D graphics. Have a look here .
just for a little more speed when normalizing
calculate 1/length instead of length and multiply your components by this factor