Given two lines in space, either they are parallel, they intersect, or they are skew (lie in parallel planes). Determine whether the lines below, taken two at a time, are parallel, intersect, or are skew. If they intersect, find the point of intersection. Otherwise, find the distance between the two lines.
L1: x = 1 - t, y = 2 - 2t, z = 2-t, -[infinity] < t < [infinity]
L2: x = 2 - 2s, y = 8 - 4s, z = 1 - 2s, -[infinity] < 5 < [infinity]
L3: x = 2 +r, y = 4 + 4r, z = 3 - 2r, - [infinity] < r < [infinity]
Select the correct choice below and fill in the answer box(es) to complete your choice.
(Type exact answers, using radicals as needed.)
O A. L1 and L2 are skew. Their distance is
O B. L1 and L2 intersect at the point ( __ __ __).
O C. L1 and L2 are parallel. Their distance is
Select the correct choice below and fill in the answer box(es) to complete your choice.
(Type exact answers, using radicals as needed.)
O A. L1 and L3 are parallel. Their distance is
O B. L1 and L3 intersect at the point
O C. L1 and L3 are skew. Their distance is
Select the correct choice below and fill in the answer box(es) to complete your choice.
(Type exact answers, using radicals as needed.)
O A. L2 and 13 are parallel. Their distance is
O B. L2 and L3 are skew. Their distance is
O C. L2 and L3 intersect at the point
