Question

Determine whether the lines

Answer 1

Answer:

skew lines

Step-by-step explanation:

Given are two lines in 3 dimension as

$L1: x=23+6t, y=12+3t, z=19+5t\\L2: x=-9+7t, y=-7+5t, z=-12+8t$

To find out whether parallel or skew or intersect

If parallel direction ratios should be proportional

Direction ratios of I line are 6,3,5 and not proportional to that of II line (7,5,8)

So not parallel

If intersect we must have same point for the two lines

Let us change parameter for II line to s to avoid confusion.  If intersecting, then

$23+6t = -9+7s\\12+3t = -7+5s\\19+5t =12+8s$

6t-7s=-32 and 3t-5s = -19

Solving

t=-3 and s =2

Check this with III equation

Left side = 19-15 =4 and right side = 12+16 =28

not equal

So there cannot be any point of intersection.

These two are skew lines