# Distance between lines

1. Aug 3, 2011

### derryck1234

1. The problem statement, all variables and given/known data

In R3, consider the line l given by the equations {x=t,y=t,z=t} and the line m given by the equations {x=s,y=2s-1,z=1}. Let P be a point on l, and let Q be a point on m. Find the values of t and s that minimize the distance between the lines by minimizing the squared distance abs(P-Q).

2. Relevant equations

[P] = A(ATA)-1AT

3. The attempt at a solution

Let the basis for l be span{(1, 1, 1)} and the basis for m be span{(1,2,0),(0,-1,1)}

From here on I actually don't know what to do:( Do I have to apply the formula to both lines?

2. Aug 3, 2011

### tiny-tim

hi derryck1234!

what's the difficulty?

P is (t,t,t) and Q is (s,2s-1,1), so minimise PQ2 (as the question says )

3. Aug 3, 2011

### derryck1234

Ok. But are you saying that I should use calculus to do that? Because in my textbook, whenever we need to use calculus, the question has a line before it saying: FOR THOSE READERS WHO HAVE STUDIED CALCULUS...

This one doesn't?

To be honest, I don't even think I remember how to do it...would it entail working out abs(P-Q), then finding the derivative and then setting it to zero?

Thanks

Derryck

4. Aug 3, 2011

### tiny-tim

Last edited by a moderator: Apr 26, 2017
5. Aug 4, 2011

### derryck1234

Thanks tiny tim. I do hope my correspondence maths course goes ok. It is not easy let me tell you...doin maths via correspondence:( Especially in South Africa!