Given two lines in , and , we can determine the angle between them with:
The angle between any two lines will always be such that .
Notice this formula is almost the same as the formula for the Angle Between Vectors, the only difference being the fact that we take the absolute value of .
This is because two vectors of equal magnitude but opposite directions generate the same exact line (given an adequate starting point).
These two lines and are orthogonal if and only if their direction vectors and are orthogonal.
That is, two lines are orthogonal if and only if their angle (in other words, if ).
These two lines and are parallel if and only if their direction vectors are parallel.
That is, two lines are parallel if and only if their angle (in other words, if .