Find the shortest distance between the two skew lines

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Homework Help Overview

The discussion revolves around finding the shortest distance between two skew lines defined by their parametric equations. The subject area includes vector geometry and spatial relationships between lines.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are exploring various approaches to determine the shortest distance, with one questioning whether the distance relates to the normal from one line to a point on the other line. Others are considering the directional vectors of the lines.

Discussion Status

The discussion is ongoing, with participants sharing ideas and questioning the validity of their thoughts. Some guidance is suggested, such as consulting examples from textbooks, but no consensus has been reached on a specific method.

Contextual Notes

There may be constraints related to the definitions of skew lines and the specific methods allowed for homework assignments, which are not fully detailed in the discussion.

frozen7
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Find the shortest distance between the two skew lines L(1) and L(2) with equations
r = (1, 2, 2) + s (4, 3, 2) and r = (1, 0, -3) + t (4, -6, -1)

How to do this? Help needed..
 
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Have you got any ideas on how you can approach this? Your book might have a few examples.
 
I have an idea but I am not sure it is correct or not.
Is the length equal to the length of the normal of either of the line to the point of another line?
 
The lines point in the direction(s) of what vector(s)?
 

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