Find the shortest distance between the solutions of the system A and the solutions of the system B

A

7x-2y+3z=-2

-3x+y+2z+5=0

I got this one, it's x+7z+12

B

-6x+2y+4z+5=0

3x-y-2z-2.5=0

-3x+y+2z+2.5=0

The answer is supposedly

z=t

y=-41-23t

x=-12-7t

When I do this however:

-6 2 4 5

3 -1 -2 -2.5

-3 1 2 2.5

>

1 -2/6 -4/6 -5/6

0 0 0 0

0 0 0 0

Now, the solution from here says

v=(-7, -23,1) u=(3,-1,-2) and computes u.v

Where do these values come from?

I also need help with the rest of the steps. I know after you get x, y, you can just use the distance formula and plug it in for 3x-y-2z-2.5, but how do I calculate for x and y?