Let us assume the direction ratios of the line be r₁, r₂, r₃.

Then:

⇒ r₁ = 2

⇒ r₂ = –1

⇒ r₃ = –2

Let us assume the direction cosines for the line be

We know that for a line of direction ratios r₁, r₂, r₃ and having direction cosines has the following property.

⇒

⇒

⇒

Let us substitute the values of r₁, r₂, r₃ to find the values of .

⇒

⇒

⇒

⇒

⇒

⇒

⇒

⇒

⇒

⇒

⇒

⇒

∴ The direction cosines for the given line is .