Let A be the point with coordinates (-4, -4, -1), let B be the point with coordinates (-2, -2, -5), let C be the midpoint of the line segment AB, let D be the point with coordinates (1,0,0), and let E be the point with coordinates (0,1,0). Let ΠΠ be the plane passing through the three points C,D,E. Suppose that the line x=y=z intersects the plane ΠΠ at the point P. Write down the first coordinate of P.

Let A be the point with coordinates (4, 4, 3), let B be the point with coordinates (2, 2, 3), let C be the midpoint of the line segment AB, let D be the point with coordinates (1,0,0), and let E be the point with coordinates (0,1,0). Let II be the plane passing through the three points C,D,E. Suppose that the line 2x - 8 = 2y - 8 = 2z - 8 intersects the plane II at the point P. Write down the x-coordinate of P. [So, for example, if you find that P has coordinates (2.5, 2, 2) then you should enter 2.5 as your answer. Please enter your answer numerically in decimal format. You will be marked correct as long as what you enter is within 0.25 of the correct answer.] Answer:

Find the equation of the plane parallel to the line r = 2i + t(-4i + 8j + 8k) and containing the points (7, 10, 7) and (6, 8, 9). (Express numbers in exact form. Use symbolic notation and fractions where needed.)

3) Find the general form of the equation of the plane that passes through the points P(-5,4,0), Q(-8,7,-5), and R(-6,9,2). >