I was asked to find the normal vector and the Cartesian equation of the plane that contains the three points A(1, 1, 1,), B(2, 3, 4) and C(1, 2, 2). I've found that the normal vector is $\displaystyle \mathbf{i}-\mathbf{j}+\mathbf{k}$ and that the Cartesian equation is $\displaystyle x-y+z = 3$. Now I'm asked whether the line r = t[1 0 0] intersects this plane. How do you find that?