[Math] Find an equation for the plane given vectors u and v

Question

I am given two vectors u = (3,1,0) and v = (3,0,1).

I am asked to find an equation for the plane containing u and v.

I have applied cross product to give me the vector perpendicular to both u and v and I want to use this as the point to substitute into my equation with either u or v to ultimately give me (a,b,c)⋅($x$-$x_0$,$y$-$y_0$,$z$-$z_0$)=$0$

Am I correct in finding my ($x$,$y$,$z$) point to substitute in by finding the cross product of both given vectors?

Thanks!

Answer 1

For any plane $P$ with equation $ax + by + cz = d$, the vector $(a, b, c)$ is perpendicular to $P$.