# How do you find two unit vectors perpendicular to the xy plane with equation 3x-4y=17?

The x-y plane has 2 natural basis vectors $\hat{x} = \left(\begin{matrix}1 \\ 0 \\ 0\end{matrix}\right)$ and $\hat{y} = \left(\begin{matrix}0 \\ 1 \\ 0\end{matrix}\right)$, and orthonormal vector $\hat{z} = \left(\begin{matrix}0 \\ 0 \\ 1\end{matrix}\right)$.
Any ordered pair that satisfies $3 x - 4 y = 17$ is a point that lies on the xy plane. Any vector that connects any 2 such points also lies on that xy plane.