Please help me. This are my homework and I am having a hard time on solving this. The answers of the questions are already provided. So you could check your work by that. Also please show all your work. I really appreciate for all your helps.

Here is my questions:

Lines: Problem 5: (Line) Find parametric equations for the following lines: (a) The line through (2, 4, 5) perpendicular to the plane 3x + 7y - 5z = 21. (Ans: x = 2 + 3t, y = 4+ 7t,z =5 - 5t) (b) The line through (2, 3, 0) perpendicular to the vectors u = i + 2j + 3k and v = 3i + 4j + 5k. (Ans: x = 2 - 2t, y = 3 + 4t, z = -2t ) Problem 6: (Line) Find the distance from point S(2,1, -1) to line, x = 2t, y = 1+ 2t, z = 2t. (Ans: 14 3 Problem 7: (Plane and Line) Find equations for the following planes: (a) Find the point of intersection of the lines x = 21 +1, y = 3t +2, z = 4t +3, and x = 5+2, y = 25+4, z=-45-1, and then find the plane determined by these lines. [Ans: -20x+12)+7=7] (b) Find a plane through the points P1: (1, 2, 3), P2: (3, 2, 1) and perpendicular to the plane 4x - y+ 2z =7. [Ans: x+6)+2=16] Problem 8: Show that the following two lines are skewed (if two lines are neither parallel nor intersecting, then they are skew) L1:x = 3+ 2t,y =-1+ 4t,z = 2-t L2: x = 3+ 2r,y =2+r,z=-2+2r