Direction Cosines and Ratios

Direction cosines and direction ratios describe the orientation of a line in three-dimensional space.

Direction Cosines

Key Property

Example: Finding Direction Cosines

Direction Ratios

Converting Between Direction Ratios and Cosines

Example: Converting Direction Ratios

Direction Cosines of a Line Through Two Points

Practice Problems

1. Find the direction cosines of a line making angles , , and with the axes.
2. Find the direction ratios of the line joining and .
3. Convert the direction ratios to direction cosines.
4. If and , find .