- #1

Pratha

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**Linear Algebra problem (Least Squares? - Distance between lines)**

## Homework Statement

We have two points R = (x,x,x) and S = (y,3y,-1). All we know is that they are on lines somewhere in 3-space and that they don't cross. Need to find an x and y that minimize || R - S ||

^{2}

## Homework Equations

A

^{T}Ax = A

^{T}b

## The Attempt at a Solution

I tried using the equation above, i.e. inverting (A

^{T}A) and multiplying both sides with that, but the resulting matrix that I got was a 2x1 matrix of zeros. This is definitely not the right answer. I also tried using (C+D(t)-b)

^{2}... for each coord and doing a partial derivative for C and D, but I ended up getting the same equation for both derivatives, which I am sure is not right.

I am very confused and not sure where to go from here.

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