Let us assume the angles that made with the positive direction of x, y, and z-axes be ,, .

Then we get,

⇒

⇒

⇒

We know that if a line makes angles of with the positive x, y, and z-axes then the direction cosines of that line is the cosine of that angles made by that line with the axes.

Let us assume that l, m, n are the direction cosines of the line. Then,

⇒

⇒

⇒

We substitute the values of in the above equations for the values of l, m, n.

⇒

⇒

⇒

⇒

⇒

⇒

∴ The direction cosines of the given line is .