Question

Use Lagrange multipliers to find the shortest distance between the line (2,4,4)+s(4,1,5) and (1,-3,2)+t(-2,3,1).

Answer 1

why do you need Lagrange multipliers?

Answer 2

that's what I'm learning atm, to be specific, I don't know how to use the parametric equation of the lines, I understand that I need to take the distance squared (denote f), and the two lines as the constraints(denote g1, g2; I think, though probably not in parametric form?) and the solve f=ag1+bg2 (a, b are the lagrange multipliers)