Planes in 3-space; Equations of planes

Hi guys,

I've got this exercise where I'm required to describe the equation of the plane determined by the fact that the following

three points lie in it: (−7, 1, 0), (2, −1, 3), (4, 1, 6).

What i've done for it is as followings:

To describe the equation of the plane we require a point in the plane and a vector $\displaystyle n$ that is orthogonal to every vector in the plane. The vectorn is said to be normal to the plane.

We suppose our point in the plane to be $\displaystyle P(x0,y0, z0)$

We chose n the normal vector to be on of our given three points.

$\displaystyle n = (4, 1, 6)$

Now we have discovered a point within the plane and a normal we can carry out the equation of the form

$\displaystyle a(x-x0)+b(y-y0)+c(z-z0)$

where $\displaystyle a,b,c = 4, 1, 6$

Well thats my attempt at the question i not quiet sure that i've answered it fully but i think i did most part correctly. I would appreciate any advice/help with it with the question it self and my answer (if it could be built on).

Thanks a lot !