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