Hi please help me with this and you can take your time. I'm not in a rush and please don't cancel the question. Thanks!

Assignment 1. Find the equation of a 2D line which...(3 marks - Knowledge) a) Passes through the points A(2, -3) and B(3, -4) b) Passes through the point A(0, -2) and is perpendicular to the vector D = (-2,-5) c) Passes through the point A(2, -4) and is parallel to the line y = -2x - 5. 2. Convert the equation of the line to the vector and symmetric forms: (3 marks - Knowledge) x = -1- 2t y = 1+ 3t z = 2+t 3. A plane, 7, has 3x - 5z + 3 = 0 as its Cartesian equation. Determine the Cartesian equation of a plane that is perpendicular to it and contains the point P(2, 9, -3). (3 marks - Application). 4. Exaplain why the planes 3x - 6y - 9z + 5 = 0 and x + 2 = 2y + 3z never intersect. (3 marks - Communication). 5. Given: two planes 71: (1 + k)x - 3y + 6z - 4 = 0 and 12: x+ (5+ k)y + 3kz + 1 = 0, Find the value of k such that (6 marks - Thinking): a) mis parallel to 12- b) 1is perpendicular to 12.Assignment A. In this section, we showed that the formula for the distance d from a point Po(xo. yo. Zo) to the plane with equation Ax + By + Cz + D = 0 is d = |AXO + Byo + Czo + DI VA? + B2 + 2 By modifying this formula, show that a formula for finding the distance from O(0, 0, 0) to the plane Ax + By + Cz + D = 0isd = IDI VA2 + B2 + C2" B. Determine the distance from O(0, 0, 0) to the plane with equation 20x + 4y - 5z + 21 = 0. C. Determine the distance between the planes with equations 7: 20x + 4y - 5z + 21 = 0 and 72: 20x + 4y - 5z + 105 = 0. D. Determine the coordinates of a point that is equidistant from 71 and 12. E. Determine an equation for a plane that is equidistant from 7 , and 72. F. Determine two values of D if the plane with equation 20x + 4y - 5z + D = 0 is 4 units away from the plane with equation 20x + 4y - 5z = 0. G. Determine the distance between the two planes 73: 20x + 4y - 5z - 105 = 0 and 74: 20x + 4y - 5z + 147 = 0