What is the plane gradient?

Question

My professor recently used the following phrase "the unknown 3D point is in a plane whose gradient is $(a,b,c)^T$". I can't seem to place his terminology anywhere on the internet. What does he mean by the gradient of the plane?

Answer 1

A plane in $\mathbb{R}^3$ is implicitly defined by $$ F(x,y,z) = ax+by+cz = \delta. $$

The points $(x,y,z)$ that verify this equation all lie in the plane perpendicular to the vector $(a,b,c)$.

The gradient of $F$ is just $\nabla F(x,y,z) = (a,b,c)$.