show that mean curvature equal zero or $v_p$ $w_p$ are are principal vectors

Question

Let $M$ be a surface in $\mathbb R^3$ , and $p$ be a point in $M$ i.e. $p\in M$ . Suppose that $v_p$ and $w_p$ are two tangent vectors to $M$ ate the point $p$ , such that $v_p.w_p=0$ and $S(v_p).S(w_p)=0$, where $S$ is the shape operator and it's defined by $S(v)=-\nabla_vU$ and $\nabla_vU$ is the covariant derivative of $U$ with respect to $v$ and $U$ is the unit normal vector field to the surface $M$. My question is show that the the mean curvature either $H=0$ or $v_p$ and $w_p$ are principal vectors. Any hint I will appreciate it.