Recall, Cartesian components have and . Therefore:

- Vectors:
We start with the basic definition of a vector from the origin to a point in Cartesian coordinates, which also tells us how to write any other vector quantity e.g. :

- Directed Length
The length element is defined according to the rule given above as:

- Directed Area
- Volume Element:
- Gradient:
- Divergence:
- Curl:
- Laplacian:

Robert G. Brown 2017-07-11