We are giving to lines:
1. Find an equation perpendicular to the two lines and passing point P(1,1,1)
2. Find Coordinates of points of intersection of the line found in #1 with planes x=-1, xz-plane
3. Parametrize the line segment joining these two points.
The Attempt at a Solution
Okay, so #1 should be relatively easy. It's merely taking the cross product of the two lines in terms of their coefficients of the slope.
My cross product of this came out to be <-2,-1,-1> So the perpendicular line is r3(w)=<1-2w,1-w,1-w)
#2 is where things get weird.
So I set 1-2w=-1 to solve for the plane x=-1. This results in w=1 which makes r3(1)=(-1,0,0)
For the xz-plane I set y=0 so I set 1-w=0. This means that w=1 and I have the same result of (-1,0,0).
Proceeding to #3, I then get a weird result of <-1,0,0>
My question is: Where did I mess up? I assume I messed up because why would they ask a question that results in this manner. I have a feeling I messed up in part #2 where I said the xz-plane must mean y=0. What could I have done differently here?
Or is my cross product miscalculated ? (I think I've checked on it multiple times..)
Thanks for any help