the plane … and a vector perpendicular to the plane

The planes $x=0$ and $y=0$ intersect in the line $x=y=0$, which is the $z$ axis. Write down a vector perpendicular to

the plane $x=0$ and a vector perpendicular to the plane $y=0$. Find ${\lambda }_1$ times the first vector plus ${\lambda }_2$ times the second. This combination is perpendicular to the line ______.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.7 Constraints and Lagrange Multipliers, #21