# shortcut to find a if a vector is normal to a plane or if it belongs to a plane?

I came to this question: which one of the following vectors is normal to the plane: x = r(1,1,2)+t(1,1-2). I know that the answer out of the four they give me is (1, -1, 0) . What I do is turning the equation into a parametric form, once it is in a parametric form i put in 3x3 matrix and I calculate its determinant, so I get the general equation of the plane , I susbtitute the points given and if it satisfies the equation wuaaala! thats the point. now well, ids tehre any shorcut that saves me from having to do the detrminant?

-
By the way, it's spelt voila. –  Rahul Feb 13 '13 at 4:20

$x$ is normal to $rv+tw$ if and only if it's normal to both $v$ and $w$. Try to prove this.

-