In this example we get

t (-105, 0, 105) + (1 - t)(8.30, 4.30, 0.00) = 
s (0, 0, 105) + (1 - s)(3.20, 4.20, 0.00)

-113.30 t + 8.30 = 3.20 - 3.20 s
   4.30 - 4.30 t = 4.20 - 4.20 s
           105 t = 105 s

The third equation implies that s = t and then the second equation becomes --

4.30 - 4.30 t = 4.20 - 4.20 t
       0.10 t = 0.10
            t = 1

So s = 1 too and substituting this back into the first equation we get --

-113.30 + 8.30 = 3.20 - 3.20
          -105 = 0

which is, of course, nonsense and we see that these three equations have no solution.

This usually happens whenever there is some measurement or even round-off error because two lines in three dimensions usually do not intersect. Although the two theoretical lines do intersect the slight changes caused by measurement error cause the measured lines to no longer intersect.