Linear Algebra (Parametric Form)

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Homework Help Overview

The problem involves finding points on two parametric lines in three-dimensional space, specifically L1 and L2, such that the distance between these points is minimized. The lines are defined by specific equations with parameters s and t, and certain values for c and d are given.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the nature of the lines, questioning whether they intersect and considering the implications of their dimensionality. There is mention of calculating a determinant as a potential step in the analysis.

Discussion Status

The discussion is active, with participants exploring the conditions under which the lines may or may not intersect. Some guidance is offered regarding the dimensionality of the problem, and there is a shared experience among participants regarding similar questions.

Contextual Notes

There is a reference to a specific course (UBC Math 152) and a link to a related question, indicating that the problem may be part of a broader curriculum context.

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Homework Statement



L1 : x = (0, 1, 2) + s(1, 0, 2)
L2 : x = (4, 2, c) + t(−2, 0, d)

If c = 5 & d = 0, find the point P on L1 and Q on L2 so that the distance between P & Q is the smallest possible.


Homework Equations



the point of intersection?


The Attempt at a Solution



well the lines aren't parallel or identical in this case so they must intersect at some point.
 
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You are thinking about two dimensions. In three dimensions non parallel lines don't have to intersect.
 
oh okayy...so then to start off would i need to find the determinant?
 
lol yeahh i am
 

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