'Show that the shortest distance between the line with equations
(x + 4)/3 = (y - 3)/2 = (z + 6)/5
and the line with equations x - 2y - z = 0, x - 10y - 3z = -7
is 1/2 sqrt 14.'
I rewrote the equations in vector form:
-4i + 3j - 6k + s(3i + 2j + 5k)
7i/2 + 7k/2 + t(-2i + J - 4k)
I found the cross product to be: -13i + 2j + 7k
(-15i/2 + 3j - 19k/2 ).(-13i + 2j + 7k) = 97.5 + 6 - 66.5 = 37
|-13i + 2j + 7k| = sqrt 222
so my answer is 37/sqrt 222.
Can someone please tell me where I'm going wrong?