I am having some difficulties doing some basic vector questions on an assignment.

a line L1 passes through (1,-1,4) and is parallel to vector (1,-1,1). Another line L2 passes through (2,4,7) and (4,5,10). obtain teh vector lines equations for L1 & L2. Do the two lines intersect, if so at what point?I think I have correctly worked out the line equations as:

for L1: r = (1,-1,4)+λ(1,-1,1) Edit: thanks to plato

for L2: r = (2,4,7)+λ(2,1,3)

But I am unsure how to work out if they intersect, and if so where?

Do i need to calculate their cartisan equations, and if so how do I then determine the intersect point.

Thanks for your time