Direction Cosines
A vector may be described in a number of ways eg
and
both describe the same vector. Both of the above notations are in a cartesian coordinate systems, but a vector may also be described in cylindrical and polar coordinates – both of this are more complicated. It is quite useful sometimes to be able to describe a vector in terms of the angles it makes with each coordinate axis – though this will not tell us the length of the vecor. Suppose we have a vector
The angles
the vector makes with the axes are illustrated above.
If
then
