How to check if a normal vector of a plane points towards or away from a certain point

Question

The problem is as follows: I have a plane defined by three points. I also have a fourth point. I now want to calculate the normalvector of the plane defined by the first three points, but i want the Normalvector to point towards the side of the plane, where the fourth point is.

My idea is to just calculate any normalvector of the plane, then drop a perpenicular from point four to the plane, and then check if the two vectors are parralell or antiparralell. Is the there a better solution without the extra step of droping the perpendicular?

Answer 1

One way of doing this is to ensure that the dot product of your normal and any vector joining a point in the plane to the fourth point is positive.

Answer 2

You can take any of the three points in your plane, say $P$ and compute the scalar product between $PQ$ ($Q$ being the fourth point) and $n$ (the candidate normal vector).

If the scalar product is positive, $n$ is correct, otherwise it is in the wrong direction.