Consider the plane defined by $2x+3y+5z=30$. Is the line parametrized by $l(s):=(-1,0,2)+s(-4,-12,18)$ for all s orthogonal to the plane?
So I know this is easy, but I'm missing one key piece. If the normal vector of the plane cross the line is equal to zero, then this confirms the line is indeed orthogonal. But now how would I cross the normal vector of the plane with this line?
And the question also asks to find a parametrization of the plane. How would I go about doing this? There are no similar examples in the textbook..