Two vectors are parallel if one is a multiple of the other. The simplest way to test that is to divide the corresponding components of the two vectors and see if it is always the same: to test if <a, b, c> and <x, y, z> are parallel check if .

Also two vectors are parallel if and only if their dot product is equal to the product of the lengths of the two vectors.

Two vectors are "neither parallel nor orthogonal " if neither of those is true- if the dot product is not 0 but also is not the product of the lengths of the two vectors.