How do you prove the following: Given the direction cosines of two lines and , then the cosine of the angle between the two lines is ?
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 a unit vector.
The angle between two vectors is given by: .
So we have: .
Therefore: .