1. Given the vector equation of a plane, (2, 1, 3) + 5(1, 1, -2) + t(4, 2, 1): a. Write the parametric equation of this plane b. Determine which of the following points are on the plane. i. (-1, O, 0) ii. (3, 5, -13) iii. (5, 2, 6) iv. (4, 1, 2) c. Find the point on this plane with an x value of 40 and y value of 25 d. Find the z-intercept of this plane. 2. Given the parametric equations of the plane x=3s+2t y=5+s+t z=4t 3. Write the vector equation of this plane. b. Find a vector perpendicular to this plane. c. Find three points that lie on this plane 3. For each of the following, find the parametric equation of the plane that a. Passes through the point (6, 1, 2) and is parallel to (-1, 2, 3) and (3, -1, 2) b. Passes through the points (2, O, 1), [-1, 3, 4), and (O, 6, 0) c. Passes through the point (4, 1, -2) and contains the line (-5, 0, 1) + 5(1, 1, -2)