1. Find the scalar equation of the plane through the points M(1,2,3) and N(3,2,-1) that is perpendicular to the plane with equation 3x + 2y + 6z +1 = 0.
2. Determine the value of k so that the line with parametric equations x = 2 + 3t, y = -2 + 5t, z = k is parallel to the plane with equation 4x + 3y - 3z -12 = 0.
3. a. Find the scalar equation of the plane that passes through the point (4, 1, 3) and is parallel to the xy-plane. b. Use what you have found in part a) to find the scalar equation of the plane if it was parallel to the xz-plane?
4. The planes A₁x + B₁y + C₁z + D₁ = 0 and A₂x + B₂y + C₂z + D₂ = 0 are perpendicular. Find the value of A₁A₂ + B₁B₂ + C₁C₂.