intersection multiplicity and tangeant space

Question

Let $V \subset \mathbb P^n(k)$ be a projective variety over an algebraically closed field $k$. Define $V'\subset Gr(n,n+1) \times \mathbb P^n(k)$ as the set of $(H,x)$ such that $H$ is an hyperplane in $\mathbb P^n(k)$ and $x \in H \cap V$. Is that true that if $(H,x)$ is a regular point of $V'$ for all $x \in H \cap V$, then the intersection multiplicity of $V$ and $H$ along each irreducible component is $1$?