Consider the plane, in $ℝ^3$ by the vector equation $$x(s, t)=(1, -1, 2)+ s(1, 0, 1) + t(1, -1, 0); s,t∈ℝ$$ Compute a unit normal vector, n, to this plane.
My attempt is the third normal vector is $\left(1,\frac{2s}{t}+1, 1 \right)$ and the unit normal vector I got is $$\frac{1}{\sqrt {3 +\frac{4s^2}{t^2}+\frac{4s}{t}}}\left(1, \frac{2s}{t}+1, 1\right)$$
HINT
$$\textbf{n} = \frac{(1,0,1)\times(1,-1,0)}{\|(1,0,1)\times(1,-1,0)\|}$$
EDIT
Since $(1,0,1) = \textbf{i} + \textbf{k}$ and $(1,-1,0) = \textbf{i} - \textbf{j}$, one has that \begin{align*} (1,0,1)\times(1,-1,0) & = (\textbf{i}+\textbf{k})\times(\textbf{i}-\textbf{j}) = -\textbf{k} + \textbf{j} + \textbf{i} = (1,1,-1) \end{align*}