3D vectors have an
x component, a
y component and a
The length of a vector:
length(v) = sqrt(v.x^2 + v.y^2 + v.z^2)
The length of a vector can be obtained with the help of the pythagorean theorem.
The direction of a vector
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.
The distance between two numbers
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