This is a hard question in the assignment for me because we never did planes and line in R^4 (yet). Thus, I managed to find the answer for a). But b) is pretty hard. Since we can't do the cross product to find the normal vector, I had to proceed through another way. I tried to arbitrarily assign a direction vector for the line in question, then try to find if it is equal to sU + tV of the plane that I founded in a). I am not entirely sure if this approach is correct to find the non parallel line to the plane in (a). Then I have no idea how to find a way to make that line not intersect the plane. Here is my attempt at this question so far:
Thanks everyone in advance!