10:12 DAVID to you 4s X SUSHI MCV4U1 Lines and Planes Test NAME: Renz L 421 Please write complete solutions on separate paper. Communication is also being assessed for correct mathematical form and style. Knowledge, Understanding, Applications 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 . 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 6. Given plane n: x + fky + 22- 9 = 0. Find k if: a) it passes through R(5, - 4, - 6). 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 the y - axes at point C. Determine this point. 2 2 2 8. Show that T = (1, 0, 1) + s(2, - 3, 1) + t(0, - 1, 1) is the same plane as T = (0, 0,2) + m(2, 4, - 6) + n(2,0,-2) O Send message