Question

Determine whether the lines l1 and l2 are parallel, skew, or intersecting. If they intersect, find the point of intersection.

Answer 1

Answer:

Step-by-step explanation:

Given are two lines equation in parametric form as

$l1: x=3-2t, y=7+4t, z=-3+8t\\l2: x=-1-u, y=18+3u, z=7+2u$

The direction ratios of the I line are -2, 4 and 8

Ii line are -1, 3, 2

These two are not proportional

Hence l1 and l2 are not parallel

Either they are skew or intersect

If intersect common point P would have coordinates as

$3-2t =- 1-u : 2t-u =4 \\7+4t = 18+3u: 4t-3u = 11\\-3+8t = 7+2u\\8t-2u = 10$

Let us solve first two equatins for u and t and check whether 3rd equation is satisfied by this.

2*(i) -ii gives u = -3

t =0.5

Substitute in III equation

8(0.5)-2(-3) = 10 so  satisifed

These two are not skew lines

The point of intersection is got by substituting either t or u

Point of intersection (2, 9, 1)