# Convert vector parametric equation to general form

Given the equation of a plane $x$ is $$x(s,t)=(0,1,1)+s(1,0,1)+t(2,1,-1)$$

How can I convert this equation into the general form $$A(x-x_0)+B(y-y_0)+C(z-z_0)=0$$

Thank you.

Hint: Write the equation as $$ax+by+cz+d = 0,$$ with $(a,b,c)$ being a normal vector to the plane. Then we find $d$ using one point of the plane, for example, $(0,1,1)$. This direction can be found computing the cross-product: $$a{\bf e}_1+b{\bf e}_2+c{\bf e}_3 = \begin{vmatrix} {\bf e}_1 & {\bf e}_2 & {\bf e}_3 \\ 1 & 0 & 1 \\ 2 & 1 & -1\end{vmatrix}.$$