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 ?

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- February 10th 2008, 02:08 AMheathrowjohnnyidentity
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 ?

- February 10th 2008, 04:31 AMSoroban
Hello, heathrowjohnny!

Quote:

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: .