equation of plane passing through line and perpendicular to xy plane

Question

I'm beginning studying 2-variables function on my own.

What is the equation of a plane passing through the line of equation

$$x +y-1=0$$

and perpendicular to the xy plane?

Can you please give me the solution and a quick reference?

Thanks

Answer 1

First $x+y_1=0$, in $\mathbf R^3$ is not an equation of a line, but an equation of a plane. I suppose you mean the line with equations $$\begin{cases}x+y-1=0,\\z=0.\end{cases}$$ The answer is obviously … $\;x+y-1=0$, since the $xy$-plane has equation $z=0$ so that these planes have normal vectors $n_1=(1,1,0)$ and $n_2=(0,0,1)$ repectively, and these normal vectors are orthogonal.