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Let $M$ be a submanifold of dimension $d ={1,...,n-1}$ class $\mathcal{C}^1$ in $\mathbb{R}^n$.

Fix $a \in \mathbb{R}^n \setminus M$.

Let $x \in M$ be such that $||x-a||=\inf \{||y-a|| \ : \ y \in M \}$, where $|| \cdot ||$ is a Euclidean norm in $\mathbb{R}^n$.

Prove that $x-a$ is orthogonal to $T_xM$.

$T_xM$ is the tangent space.

Thank you for your help.