How would you show that a vector is normal to a plane in 3D space?

There are 2 main methods for finding a normal vector.

1. If you know two vectors that lie in the plane e.g. (a,b,c) and (d,e,f), we can find a normal vector by calculating the vector/cross product of (a,b,c) and (d,e,f). This works because the vector product produces a new vector perpendicular to both your starting vectors, so it must be at right angles to the plane.

2. If on the other hand you know the Cartesian equation of a plane, which looks like (ax)+(by)+(cz)=0, then the vector (a,b,c) is a normal vector!