Please write complete solutions on separate paper. Communication is also being assessed for correct mathematical form and style. Knowledge, Understanding, Application RT 1. Consider the plane given by m: - 3x + 4y - z - 24 = 0 a) State the normal vector to this plane. b) Determine if the point M(2,0,3) lies on the plane i. 2. Find the Cartesian equation of the plane that passes through the points A(- 3. - 2,0) and B(1,3, - 1) and C[- 1,2,4). 3. Determine the parametric equations of the line whose direction vector is perpendicular to the plane - 2x + 4y - 52 + 2 = 0 and passes through the point (1.2.1). 4. Determine the point (s) of intersection of the line and plane: (x, y. z) = (3,1,1) + t(2, - 1,2),tER 3x - 4y - 52 = 0 5. Solve the following systems of equations. Describe their intersection geometrically. - x + 5y - 2 = 15 - x+ y - 52 = 27 2x + 4y - z = 13 Thinking R 6. Given plane m: x + ky + 2z - 9 = 0. Find k if: it passes through R(5, - 4, - 6). b] It is perpendicular to plane m1 : 2x + 4y - 3z = 0 7. The plane with the equation r = (1,4,3) + s(1,2,5) + t(1, - 1,3) intersects they - axes point C. Determine this point. 8. Show that r = (1, 0, 1) + s(2, - 3, 1) + t(0, - 1, 1) is the same plane as F = (0, 0, 2) + m(2, 4, - 6) + n(2,0,-2)