Show that the two lines

L1 : (3,2,-1) + t(1,6,1) and L2 : (1,0,1) + t(1,-3,-4), where t ∈ R

do NOT intersect in R3 (careful: in R3 non-parallel lines may not intersect), and find the distance between the two lines. HINT: find the equation of the plane passing through line L1 and parallel to L2 by using one point on L1 and a normal vector to the plane – or in other words, a vector perpendicular to both L1 and L2 .

Question

Show that the two lines

L1 : (3,2,-1) + t(1,6,1) and L2 : (1,0,1) + t(1,-3,-4), where t ∈ R

do NOT intersect in R3 (careful: in R3 non-parallel lines may not intersect), and find the distance between the two lines. HINT: find the equation of the plane passing through line L1 and parallel to L2 by using one point on L1 and a normal vector to the plane – or in other words, a vector perpendicular to both L1 and L2 .

anonymous · Answer

I really need the answer and appreciate your help :)