Direction Angles
Here you can learn how to determine the angle between a vector x in 
and any of the coordinate axes. For example, in 
x has two direction angles, the vector 
from the first coordinate axis, and the angle 
from the second coordinate axis.
Definition For 1 
, the -th direction angle of a vector x in is
, the -th direction angle of a vector x in is
To compute direction angles we use the dot product, as in proposition below.
Proposition The -th direction angle of x in is
-th direction angle of x in is
The cosines of the direction angles of a given vector are related by the following formula.
Proposition Given a nonzero vector x in , let 
denote its -th direction angle. Then
Exercises on direction angles
- Previous section: The dot product
- Parallel section: Projection of a Vector on a Line
- Parallel section: Hyperplanes
- Parallel section: Distance of a Point from a Hyperplane