# Linear Algebra: Distance problems.

1. Jun 1, 2009

### haux

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

Let P=(5,5,−1), Q=(6,7,2), R=(7,6,0) and S=(7,3,−2). Let l1 be the line passing through P and Q, and let l2 be the line passing through R and S.

(i) The distance between R and l1 is _____

(ii) The distance between l1 and l2 is _____

2. Relevant equations
projd(v) =
[(v • d)] d
[||d||2]

3. The attempt at a solution

1. Since it said l1 was represented by points PQ and l2 by points RS, I took Q-P and S-R which resulted in:

l1 = (6,7,2)-(5,5,-1) =(1,2,3)
l2 = (7,3,-2)-(7,6,0) = (0,-3,-2)

Now that we have two lines represented by three points, for the first part of the question, can we use the projection formula for 'R'? Also, even though l1 and l2 are now represented by three points, are we supposed to combine all the original points somewhere down the road to create an equation of the line? Thanks.

2. Jun 2, 2009

### tiny-tim

Hi haux!
Hint: you'll also need either RP or RQ