4. A line can either lie on a plane, lie parallel to it or intersect it. a. Determine, if there is one, the point of intersection between: the line given by the equation x-3_y-1 =-15 2 4 and the plane given by the equation [x, y, z] = [-2, -7, 5] + s[2, 6, 3] + t[1, 4, -1] b. Determine the angle between the line and the plane. GO TO: THE DROPBOX AND UPLOAD YOUR WORK. c. Give the equation of a plane and three lines, one of which is parallel to the plane, one of which lies on the plane, and one of which intersects the plane. Explain your reasoning and include a LanGraph. 5. The angle between two planes can also be determined. a. Find the angle between the planes given by the equations [x, y, z] = [-2, -7, 5] + s[2, 6, 3] + t[1, 4, -1] and [x, y, z] = [1, 6, 2] + s[3, -2, 5] + t[5, 1, -6] b. Give the equations of two planes that meet at a 90" angle. Explain your reasoning and Include a LanGraph of your planes. 6. A third plane can be found that passes through the line of intersection of two existing planes. a. Two planes are given by the equations 2x - 3y + z - 6 =0 and -3x + 5y + 42 +6 = 0. Find the scalar equation of the plane that passes through the line of intersection of these two planes, and also passes through the point (1, 3, -1). b. Give the equations of two planes. Create a third plane that passes through the line of intersection of the original two and which is parallel to the z-axis. Explain your reasoning and include a LanGraph of your planes. 7. Three planes can intersect in a number of different ways. For each of the combinations below, find the single point of intersection if there is one. If there isn't, explain how the planes do intersect. x-3y-2:+3 = 0 a. *, : -4x+2y+3:-7 = 0 5x +4y+=-5 = 0 * : 3x -2y+2:-8 = 0 b. *, : -4x+y+3:+3 = 0 *, : 2x-3y+7=-13 = 0 8. Give the equations of three planes that meet in three lines. Explain your reasoning and include a LanGraph of your planes that allows you to see the triangular prism created