A plane is a two dimensional vector space.
A plane has a dimension of two because two coordinates are needed to specify a point on it.
# A more familiar way to specify a plane
{(x, y, z) : ax + by + cz = 0}
# Using dot-product, the above equation becomes a set of vectors
# satisfying a linear equation with right-hand side zero
{[x, y, z] : [a, b, c] * [x, y, z] = 0}
The intersection of the two following plane:
is
The translation of a plane translate it in a way that it doesn't contain the origin.
You can express such plane as
Vector addition is used to defined a set of points forming an plane that not necessarily go through the origin.
You translate the plane by adding a vector c [0.5, 1] to every point in the plane.
abbreviated: <math>c + nu</math>
The result is a plane through c instead of through origin.
The solution set of an linear equation: