Find the Cartesian equation of the plane which contains the

Find the Cartesian equation of the plane which contains the point (5, 1, 3) and has normal vector n = (1, 4, 2)T . Find also a vector (parametric) equation of this plane.

Solution

Let a point on the plane be r and given point be r0 and the normal vector is n so equation of plane is

(r-r0).n=0

So

(x-5)-4(y-1)+2(z-3)=0

or

x-4y+2z=7

Let, y=s,z=t

So,

x-4s+2t=7

x=4s-2t+7,y=s,z=t