Question

Determine whether the lines x=1+2t, y=3t, z=2-t and _______ are parallel, skew, or intersecting. If they intersect, find the point of intersection.

Answer 1

The given lines x=1+2t, y=3t, and z=2-t are skew.

Step-by-step explanation:

The given lines are x=1+2t, y=3t, z=2-t, and _______. To determine whether the lines are parallel, skew, or intersecting, we can compare their direction vectors. The direction vector of the line x=1+2t is (2,0,0), the direction vector of the line y=3t is (0,3,0), and the direction vector of the line z=2-t is (0,0,-1). The lines are skew if none of the direction vectors are proportional and intersecting if all the direction vectors are proportional. If two of the direction vectors are proportional, the lines are parallel.

By comparing the direction vectors, we see that (2,0,0), (0,3,0), and (0,0,-1) are not proportional. Therefore, the lines are skew.