I was given that
$F(x,y,z)=\left<x+y, zx−yx, y^2-z^2\right>$
and that I needed to find the tangent, normal, and binormal vectors at $P(1, 1, 1)$.
I know that about $T(t)=F'(t)/\|F'(t)\|$, etc. But all that formulas talks about $\mathbb{R}\to \mathbb{R}^m$, and my function is defined on $\mathbb{R}^m\to \mathbb{R}^m$; $\mathbb{R}^3\to \mathbb{R}^3$
It is possible to determine $T$, $N$, and $B$ ? And, how? Please be explicit.