please make sure answers are correct .. most of the answers solved by coursehero tutors are incorrect... my quizzes need good grade this time and solve them on papers with pen so i can understand plus make sure to be good hand-writing that kids can understand ... don't use professional handwriting that looks like chicken feet scratches...

9. Find the distance between the 2 parallel planes: . J-3x+6y+72=1 decimal places. 6x-12y-142=25' . You can give the answer out to 2 10. Find the parametric equation for the line going from A (0, 0, z) to B (3, 5, 7) and parallel to the plane 2x + 4y+6z =5. Note that the z-component in point A is unknown so it must also be determined. 11. Object A travels along the line x+1=4t y-3=t z-1=0. Object B, along the line x+13=12t y-1=6t z-2=3t . Find their intersection point. 12. Determine the point where the line x =4+3t y=2-t z=3+t passes through the plane xty+z-4=0 13. Find the equation for the plane that contains the point A(2, -4,6) and is perpendicular to the line x=2+4t y=4-2t z=6+3t. Express your answer in the form ax + by + c= + d =0 14. Convert the rectangular coordinate equation x + y + z =4z to cylindrical coordinate. Simplify your answer when possible.7. A roller coaster car weighing W = 1200/bs enters a turn with bank angle O as shown. During the turn, the car generates a normal force N N = 1400/bs . If the vertical component of this normal force equals to the weight of the car, determine the bank angle 0. IV 8. A hydrofoil boat has the front foil set at 0, = 50 and the rear foil set at 0, = 7" . The front foil generates a normal force F, = 7500 N and the rear foil, F2 = 3000 N . For the geometry shown, determine the total torque vector created by the front and rear foils at point O. Clearly provide the position components and th force components of the front and rear foils. 15 m 4 m O F1 2 w