Hello I need some help with these 3 questions. If you could please show me all your work on a separate sheet of paper with the solutions/answers that would be great!

5. Determine vector and parametric equations for the plane containing the point A(2, -3, 1) and parallel to the plane with equation (x, y, z) = (2, 1, -3) + s(8, 2, -1) + t(3, -2, 4). Show your work. 6. Determine vector and parametric equations for the plane through the point P(0, -2, 0) and parallel to the xy-plane. Show your work. 7. Does the line with equation (x, y, z) = (5, -4, 6) + u(1,4,-1) lie in the plane with equation (x, y, z) = (3, 0, 2) + s(1, 1,-1) + t(2, -1, 1)? Justify your answer algebraically