Normal Vector

linear-algebra

Definition

Normal Vector

Let $V$ be an inner product space. A vector $0\ne n\in V$ is a normal vector to a set $S$ at a point $p$ if it is orthogonal (perpendicular) to the tangent space of $S$ at $p$.

Orthogonality Condition

For every vector $v$ that is tangent to $S$ at point $p$:

$$⟨n,v⟩=0$$