This is a very noob question, but can someone please give me an example of finding the normal vector to a surface (if this is the word in English) which is defined by three points in it. I know that there are two ways - the first to find the equation of the surface and to take the coefficients, and the second - to find two vectors from the points and then to multiply them vectorly (I'm almost sure that this isn't the name for this operation x in English), but I still have a little difficulties and an example with concrete points will be very helpful!
Thank you very much in advance and please excuse me for my stupidity and bad English!
Suppose you have points $A(0,0,0),B(0,1,0)$ and $C(1,0,0)$. We need to find the normal to the unique surface(which is a plane for 3 points) passing through these points.
Now, $\vec{AB}, \vec{AC}$ both lies in the plane and cross-product of any two non-zero vectors is a vector normal to both the vectors, and hence normal to the surface containing the vectors.
Thus required vector is $\vec{AB}$ x $\vec{AC}=(\vec j) $ x $(\vec i)=-\vec{k}$
So any scalar multiple of this vector=$\lambda \vec k$ is normal to the surface.