Hello I need some help with these 10 questions. If you could please show me all your work on a separate sheet of paper with the solutions/answers that would be great!

1. Determine vector, parametric and, if possible, symmetric equations for the line through the point (2, -2, 1) with direction vector m = (4, -3, 5). 2. Determine vector, parametric and, if possible, symmetric equations for the line through the point (-2, 2, 5) and parallel to the line through the points A(2, -3, 4) and B(3, 2, -1). 3. Determine vector and parametric equations for the z-axis. 4. Determine vector and parametric equations for the line with symmetric equations x - 2_y+5 z-1 3 -2 5. Determine symmetric equations for the line F = (-2, 3, 0) + t(-1, -3, 2). 6. Show that the lines *-3_y +3_z-1 and *+2_y-1_z+6 - 2 6 are parallel. 4 4 -8 -12 7. Determine the coordinates of three non-trivial points on the line F = (1, -2, 3) + t(2, -1, 4). Show your work. 8. Determine if the point A(-2, 1, 2) lies on the line F = (1, 3, 0) + t(-2, 1, 1). 9. Determine if the point (-3, 2, -2) lies on the line with parametric equations x = 1 - 2t, y = 4 - t, z = 2 + 3t. 10. Determine vector, parametric and, if possible, symmetric equations for the line through Q(2, -1, 3) and the mid-point of the line segment from L(3, -2, 5) to M(1, 4, -7)