Consider in $\mathbb{R}^3$ the plane $N: x+y+z=0$ and the sphere $S: (x-a)^2+(y-b)^2+(z-c)=r$, where $r$ is fixed.
The intersection $N\cap S$ is the disk embedded in $\mathbb{R}^3$. I would like to know the (a) tangent vector of $D$ at its boundary.
Write $n_D(x)$ the tangent at $x$ of $D$, $n_S(x)$ the tangent at $x$ of $S$, $n_N(x)$ the tangent at $x$ of $N$.
Do we have that $n_D(x)$ is linearly dependant of $n_N\wedge n_S$ ?
I feel like the notion of tangent vector in this case is not well defined.