Hello, heathrowjohnny!

Line has vector: . . . . and: .Given the direction cosines of two lines: . and ,

then the cosine of the angle between the two lines is:

. .

Line has vector: . . . . and: .

. . That is, a set of direction cosines always forms aunit vector.

The angle between two vectors is given by: .

So we have: .

Therefore: .