Determine whether the lines l1: x=18+6t, y=7+3t, z=13+3t and l2: x=−14+7ty=−12+5tz=−8+6t intersect, are skew, or are parallel. if they intersect, determine the point of intersection; if not leave the remaining answer blanks empty.

skew lines

Step-by-step explanation:

we are given 2 lines in parametric form as

L1:x=18+6t,y=7+3t,z=13+3t and L2:x=−14+7ty=−12+5tz=−8+6t

If the lines intersect then the two points must be equal for one value of t.

Let us try equating x,y and z coordinate.

when we equate y coordinate we get

Since we get two different t we find that these two lines cannot intersect.

Comparing direction ratios we have

I line has direction ratios as (6,3,3) and second line (7,5,6)

These two are not proportional and hence not parallel

So these lines are skew lines

answer: 45

i don't think there is enough