Question

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=1-2t,z=2-2t, -infinity is less than t is less than infinity

L2: x=-5-2s, y=-13-4s, z=2-4s, -infinity is less than s is less than infinity

L3: x=1+2r, y=1+5r, z=2+r, -infinity is less than r is less than infinity

Select the correct choice below and fill in the answer box(es) to compare your choice.

(Type exact answers, using radicals as needed)

1.

(A) L1 and L2 intersect at the point (__ ,__ ,__ )

(B)L1 and L2 are parallel. Their distance is ____

(C)L1 and L2 are skew. Their distance is _____

2.

Select the correct choice below and fill in the answer? box(es) within your choice.

A. L1 and L3 are parallel. Their distance is ____.

B. L1 and L3 interesct at the point (__,__,__)

C. L1 and L3 are skew. Their distance is ____.

3. Select the correct choice below and fill in the answer? box(es) within your choice.

A. L2 and L3 are skew. Their distance is _____.

B. L2 and L3 are parallel. Their distance is ____.

C. L2 and L3 intersect at the point (__,__,__)

Answer 1