Unit Vectors:

1. We denote unit vectors as: _x = / ||

   This means that the unit vector _x is a vector of length 1, pointing in the same direction as the vector . Unit vector are dimensionless.

2. For any vector , we can then write from the above equation = || · _x := x · _x

   where || := x is the length of the vector.

3. Orthogonal unit vectors: The unit vectors in the directions of a cartesian coordinate system form an orthonormal set. This leads to the following rules:
   • Scalar products: _x · _x= _y · _y= _z · _z= 1
     _x · _y= _y · _z= _z · _x= 0
   • Vector products:
   _x x _x= _y x _y= _z x _z= 0
   _x x _y= _{z
   y} x _z= _{x
   z} x _x= _y

© W. Bauer, 1999