Hello I need some help with these 6 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. a) Determine the symmetric equations for the line through P(-3, -3, 2) and parallel to the line with equation 7 = (6, 1, -1) + t(-2, 1, 3). b) Determine two (2) other points on this line. 2. Find the value of k so that the lines below are perpendicular x-3 = y+6 = 2+3 y+8 3 k- 1 2k and * +7 = 2+9 -2k 3. Determine parametric equations for the plane through the points A(2, -4, 1), B(-1, 1, 3), and C(3, 3, 2). 4. Determine a vector equation for the plane that is parallel to the yz -plane and passes through the point (4, -1, 3). 5. Determine a scalar equation for the plane through the points M(1, 2, 3) and N(3 ,-2, -1) that is perpendicular to the plane with equation 3x + 2y + 6z + 1 = 0. 6. Show that the line with parametric equations x = 3 + 8t, y = -5 + t, z = 1 + 3t does not intersect the plane with equation 2x - y - 5z - 2 = 0