#9 Review Exercise1. Determine vector and parametric equations of the plane that contains thepoints A(1, 2, -1), B(2, 1, 1), and C(3, 1, 4).2. In question 1, there are a variety of different answers possible, depending onthe points and direction vectors chosen. Determine two Cartesian equationsfor this plane using two different vector equations, and verify that these twoequations are identical.3. a. Determine the vector, parametric, and symmetric equations of the linepassing through points A(-3, 2, 8) and B(4, 3, 9).b. Determine the vector and parametric equations of the plane containing thepoints A(-3, 2, 8), B(4, 3, 9), and C(-2,-1, 3).c. Explain why a symmetric equation cannot exist for a plane.4. Determine the vector, parametric, and symmetric equations of the line passingthrough the point A(7, 1, -2) and perpendicular to the plane with equation2x - 3y + z-1 = 0.5. Determine the Cartesian equation of each of the following planes:a. through the point P(0, 1, -2), with normal = (-1, 3, 3)b. through the points (3, 0, 1) and (0, 1, -1), and perpendicular to the planewith equation x-y-z+1=0c. through the points (1, 2, 1) and (2, 1, 4), and parallel to the x-axis6. Determine the Cartesian equation of the plane that passes through the origin andcontains the line = (3, 7, 1) + (2, 2, 3), tER.7. Find the vector and parametric equations of the plane that is parallel to theyz-plane and contains the point A(-1, 2, 1).8. Determine the Cartesian equation of the plane that contains the line7=(2, 3, 2) + t(1, 1, 4), tER, and the point (4, -3, 2).9. Determine the Cartesian equation of the plane that contains the following lines:L₁:7=(4, 4, 5) + 1(5, -4, 6), te R, andL₂:7 (4,4,5) + s(2, -3, -4), SER10. Determine an equation for the line that is perpendicular to the plane3x - 2y + z = 1 passing through (2, 3, -3). Give your answer in vector,parametric, and symmetric form.11. A plane has 3x + 2yz + 6 = 0 as its Cartesian equation. Determinethe vector and parametric equations of this plane.NEL

Explanation of the answer is as follows

7=(2, 3, 2) + t(1, 1, 4), tER, and the point (4, -3, 2). of the plane that contains the line 9. Determine the Cartesian equation of the plane that contains the following lines: L₁:7=(4, 4, 5) + 1(5, -4, 6), te R, and L₂:7 (4, 4, 5) + s(2, -3, -4), SER 10. Determina OR