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Introduction
Vectors for geometry:
straight line trajectories;
surfaces;
...
Dot (scalar) product:
Cross (vector) product:
and normal to both vectors.
Line through point
P
parallel to vector
:
The parameter
can be eliminated to give two scalar equations.
Plane through point
P
normal to vector
:
Each equation ordinarily reduces the dimensionality by one: 3D (space)
2D (plane)
1D (line)
0D (point)
nothing.
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:
can be eliminated to give two scalar equations.
:
2D (plane) 1D (line) 0D (point) nothing.
:
can be eliminated to give two scalar equations.
:
2D (plane) 1D (line) 0D (point) nothing.