# Finding a line not parallel to a plane and that also does not intersect that plane in R^4

This is for my linear algebra assignment:

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:

You have vectors $\vec{AB}$ and $\vec{AC}$. Try finding some other 2 vectors independent to them.
for example $\vec{AB}$(1,3,-2,2),$\vec{AC}$(0,1,0,2),$\vec{m}$(1,0,0,0),$\vec{n}$(0,0,1,0). It is really simple finding it, try some random vectors.
Now you move from A by vector $\vec{m}$ it is point (2,0,1,0) and put a line in direction of $\vec{n}$. So parametric expression for the line is (2,0,1+k,0).