Introduction

Vectors for geometry:

• straight line trajectories;
• surfaces;
• ...

• Dot (scalar) product:

  

• Cross (vector) product:

  

  and normal to both vectors. Seen from below:

  

• Line through point P parallel to vector :

  

  

• Plane through point P normal to vector :

  

  

• Each equation ordinarily reduces the dimensionality by one: 3D (space) 2D (plane) 1D (line) 0D (point) nothing.