point $(1,2,3)$ and
    has normal vector $(4,5,6)$, then give an equation of the
    plane. <div class="review-answer">An equation of the plane is
    $4(x-1)+5(y-2)+6(y-3)=0$. If $(x,y,z)$ is any point in the
    plane, then the vector $(x-1,y-2,z-3)$ is a vector in the
    plane, and hence orthogonal to $(4,5,6)$. The dot product of
    these two vectors should be equal to zero, which is why the
    plane's equation is $(4,5,6)\cdot (x-1,y-2,z-3)=0$.</div>
  </div>

  <div class="problem">
    Consider a