Question

also how can you find the normal of a plane given the parametric equation of a plane?

Answer 1

If you are given the parametric equation of the plane like this
\[x(t) = x _{0} + at\]
\[y(t) = y _{0} + bt\]
\[z(t) = z _{0} + ct\]

then the normal vector is
n = <a, b, c>