Vectors

• 2D vectors have the components x, y
• 3D vectors have the components x, y, z, w
• 4D vectors the components x, y, z, w

length(v) = sqrt(v.x^2 + v.y^2)         // 2D Vectors
length(v) = sqrt(v.x^2 + v.y^2 + v.z^2) // 3D Vectors

The length of a vector can be obtained with the help of the pythagorean theorem.

normalize(v) = v / length(v)

Like with numbers (aka 1D vectors) the direction of a vector can be calculated by dividing the vector by the length of the vector.

distance(a, b) = length(b - a)

The dot product of two vectors a = [ax, ay, az] and b = [bx, by, bz] is defined as

dot(a, b) = ax * bx + ay * by + az * bz