Questions 1. Determine the scalar equation (Ax + By + Cz + D = 0) of a plane through the point (4, 1, 2) and having normal vector = (3, -2, 2). 2. Find the scalar equation of the plane through the points Q(2, 3, -1), R(-1, 5, 2) and S(4, 2, 2). 3. A plane contains the point (1, 1, 4) and is perpendicular to the line with vector equation = (1, -1, -2) + t(2, -3, 1). Determine the scalar equation of the plane. 4. Determine the scalar equation of the plane with vector equation = (3,-1,4) +s(2,-1,5) + t(-3,2,-2). 5. Determine if the point P(1, 2, 3) lies in the plane with equation 2x + 3y - 4z+4=0. 6. 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. (Please click on the instructor's YouTube video lesson for help with this question). 7. Determine the value of k so that the line with parametric equations x = 2 + 3t, y = -2+5t, z=kt is parallel to the plane with equation 4x + 3y - 3z-12 = 0. 8. a. Find the scalar equation of the plane that passes through the point (4, 1, 3) and is parallel to the yz-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? 9. The planes A1x + By + Cz + D = 0 and A2x + B2y + C2z + D2 = 0 are perpendicular. Find the value of A1A2 + B1B2+C1C2.