I have the following problem:
Determine if these lines intersect. If so, find their point of intersection.
$L1 = (4,5,-1)+t(1,1,2)$
$L2 = (6,11,-3)+s(2,4,1)$
I managed to solve this problem by 1) Doing a cross product, seeing that the result is not 0, and 2) plugging in a bunch of $t$'s and $s$'s by trial-and-error until I ended up finding the point $(2,3,-5)$, as the answers to many other similar homework questions say to do (like this one).
This process took me a very long time. As opposed to trial and error, is there a method that will always give me the point of intersection of two lines in either cartesian, parametric or symmetric form?