Vector and parametric equations of a plane
I am having trouble with a question. I have NO IDEA how to go about finding the solution, so any help is greatly appreciated!
Find a vector equation and parametric equations of the plane that contains the points M(2, 1, 3) and N(-1, 5, 7) and is perpendicular to the plane x + 2y + 3z + 4 = 0.
What I know
So I know how to find the vector equation of a plane if I am given 3 points (or 2 direction vectors and a point) on the plane. I also know how to find the parametric equation given the same thing.
My theory on how to solve this is using the two points given to get a direction vector (3, -4, -4).
I know that the Cartesian equation of a plane is in the format Ax + By + Cz + D = 0. The capital letters (A, B, C) are the normal to the plane the Cartesian vector is referring to (so, in this case, it would be the second direction vector I need). The x y z are a point on that plane. I do not know how to combine this information in order to solve the problem though!
Thank you for reading, and SUPER thank you if you help (Clapping)