You don't quite have it right; your example should be like this:
'Now there are 3 holes on either side of the beam their positions referenced with relative coords to the beam centre point, so that the position of 3rd hole xc is determined by the positions of the first 2 holes;
xa = 2"
xb = 3"
xc = (xa*xb) = (2"*3") = 6"" (inches squared, but it should be just inches)
...
In freshman physics we learn that if the units don't work out as expected at the end of a calculation, you've done something wrong.