# Various other curiosities

### Equation of a Line in an Affine Space defined by two point P and Q and t a
real

## set of point of the form (1-t) P + t Q

### Equation of a Plane in an Affine Space defined by three not collinear point
P, Q and R

## set of point of the form (1-s) ((1-t) P + t Q) +s R

## Vector and affine linear subspace are resp. vector and affine space

V : Non empty subset which is stable through the addition and the multiplication
by a real

A : such as the set of the difference between any element of A is a linear
vector subspace

### Example

## Vector subspace of R4

/ x
| y
| z
\ 0

## Affine Subspace of R4 : standard affine 3 space

/ x / x1 - x2
| y v1 - v2 = | y1 - y2 belongs to the previous
| z | z1 - z2 vector subspace of R4
\ 1 \ 0