The direction cosines of a directed line can be defined as cosine values of the angles made by the directed line with the x-axis, y-axis and z-axis respectively.
Explanation:
Consider a directed line \(\overrightarrow{OA},\) in the three dimensional space.
If α, β and γ be the angles made by the directed line \(\overrightarrow{OA}\) with the x-axis, y-axis and z-axis respectively.
In the above figure, the direction cosines of line OA are:
Cos α = cosine of the angle between x-axis (OX) and the directed line \(\overrightarrow{OA}.\)
Cos β = cosine of the angle between y-axis (OY) and the directed line \(\overrightarrow{OA}.\)
Cos γ = cosine of the angle between z-axis (OZ) and the directed line \(\overrightarrow{OA}.\)
