I'm a bit uncertain about this question and would like some help, as I don't have the correct answer. Have I done this correctly?(adsbygoogle = window.adsbygoogle || []).push({});

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

What is the shortest distance between the two lines A = (1,2,3) + t(0,1,1) and B = (1,1,1) + s(2,3,1)

3. The attempt at a solution

My reasoning: The vector AB is shortest when AB is orthogonal to BOTH A and B.

Therefore the scalar product AB [tex]\circ[/tex] A = AB [tex]\circ[/tex] B = 0. That gives a system with two equations

AB = (2s, -1+3s-t, -2+s-t)

AB [tex]\circ[/tex] A = -3+4s-2t=0

AB [tex]\circ[/tex] B = 14s-5-4t=0

which when solved gives s = -1/6 and t = -11/6.

I now seek |AB|, or the LENGTH of the vector.

Substituting s and t with the corresponding values and then using Pythagoras gives:

|AB| = sqrt(1/3)

Is this correct? Is there perhaps an easier way to do this?

Danke schÃ¶n!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Shortest distance between two lines

**Physics Forums | Science Articles, Homework Help, Discussion**