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.

Answer:skew linesStep-by-step explanation:we are given 2 lines in parametric form asL1:x=18+6t,y=7+3t,z=13+3t and L2:x=−14+7ty=−12+5tz=−8+6t[tex]L1:x=18+6t,y=7+3t,z=13+3t \\ L2:x=-14+7t,y=-12+5t,z=-8+6t[/tex]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.[tex]18+6t = -14+7t\\t=32\\[/tex]when we equate y coordinate we get[tex]7+3t =-12+5t\\2t =19\\t =9.5[/tex]Since we get two different t we find that these two lines cannot intersect.Comparing direction ratios we haveI line has direction ratios as (6,3,3) and second line (7,5,6)These two are not proportional and hence not parallelSo these lines are skew lines