Normal to a plane My textbook makes a quick, unproven claim that if a vector P is orthogonal to /one/ vector that lies on a plane G, then P is normal to the plane. My question is, is this a mistake? Wouldn't you need P to be orthogonal to two vectors on G not contained in the same line, for it to be normal to G? 
Thanks!

You're quite right: it's clearly a mistake, since the line $y=z,x=0$ is orthogonal to the $x$-axis but not to the $xy$-plane. Your suggested revision is correct, because if a vector is normal to $u$ and $v$, it's normal to everything in the span of $u$ and $v$.
