maybe this comes a little bit late ...
If then the equations of the lines can be written like this:
If and are the position vectors to the fixed points of the lines, and the direction vectors of the lines and is the normal vector to and then the distance d is calculated by:
2. Now plug in all the values you know into the equation to calculate the distance:
to a): I assume that you have written your problem correctly.
If so you can simplify the given equations:
Then these equations with the given restriction describe a straight line connecting the points A(8, -12, 2) [for k = 0] and B(-6, 0, 4) [for k = 2]:
The equation of the line where the points A and B are placed on is:
to b) I have no idea what to do - sorry!