Write a generic vector parametric equation and a generic Car

Write a generic vector parametric equation and a generic Cartesian equation of a plane in R^3.

Solution

Generic Cartesian equation of a plane in R³ : ax+by+cz+d=0;
Generic Vector equation of a plane in R³ : (r - a) . n^ =0
where r is the generic vector xi + yj + zk
a is a specific vector (for eg. 2i + 3j - k)
and n is the normal vector to the plane