Determine the interaction of the line of intersection of the planes x + y - z = 1 and 3x + y + z = 3 with the line of intersection of the planes 2x - y + 2z = 4 and 2x + 2y + z = 1.

Answer 1

Find the line of intersection of the first two planes, using the method I showed you yesterday.
Do the same for the second pair of planes.

Write each line in parametric form but use a different parameter, use t in the first one, k in the second

Now there are three possibilities.
1. the two lines are parallel
2. The two lines intersect
3. the two lines miss each other, and are not parallel

(A fourth trivial case would be if the two lines end up the same line)

for #1, look at the direction numbers. Are they the same?

If not set the x's and the y's of the two sets of parametric equations equal to each other, you should be able to solve for t and k
If the values of t and k also satisfy the parametric equations for z, then they actually intersect in a point, if not, they will miss each other.

(How about letting me know if you are getting this stuff. I have now helped you with about 6 of these vector problems but you have not replied if you are following this .)