A plane may be considered as a mapping
where X is called a vectored valued function of 2 real variables. The scalars s and t are called parameters and eq(2.6) is called a parametric, or vector, equation of the plane. For vectors in Rn, eq(2.6) represents n scalar equations. Taking as example the case R3 and write
Eliminating s and t gives a linear equation of the form
known as the Cartesian equation of the plane.
Let with , and .
The vector equation is
which is equivalent to 3 scalar parametric equations
To obtain the Cartesian equation, we solve s, t from the 1st and 3rd eqs
Substituting them into the 2nd eq gives