How to find the intersection point between two lines

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Discussion Overview

The discussion revolves around finding the intersection point between two lines represented in parametric form. Participants explore the implications of using different parameters for the lines and clarify the conditions necessary for determining an intersection.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests using different parameters for the two line equations to find a common point of intersection.
  • Another participant expresses confusion over the use of the same parameter for both lines, questioning the validity of the original question.
  • A later reply clarifies that while the general form of a line equation uses a single parameter, distinct parameters must be used for intersecting lines.
  • There is a mention of a potential typo in the original post, indicating a misunderstanding of the equations presented.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the initial question's validity, with some suggesting it contains a mistake while others argue that the question itself is not erroneous but rather reflects a misunderstanding of parameter usage.

Contextual Notes

There is an unresolved discussion regarding the necessity of distinct parameters for the two lines and the implications of using the same parameter in the context of finding an intersection point.

Raerin
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How to find the intersection point between two lines?

line 1: r = (3,1,-1) + s(1,2,3)
line 2: r = (2,5,0) + s(1,-1,1)
 
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Raerin said:
line 1: r = (3,1,-1) + s(1,2,3)
line 2: r = (2,5,0) + s(1,-1,1)

Hey Raerin! ;)

Let's use a different parameter in both of those line equations.

line 1: r = (3,1,-1) + s(1,2,3)
line 2: r = (2,5,0) + t(1,-1,1)

We're looking for an $s$ and a $t$, such that the resulting r is the same...Btw, perhaps you could also put your question inside your post instead of only as the title of the thread.
Your post looks a bit out of context now. :o
 
I like Serena said:
Hey Raerin! ;)

Let's use a different parameter in both of those line equations.

line 1: r = (3,1,-1) + s(1,2,3)
line 2: r = (2,5,0) + t(1,-1,1)

We're looking for an $s$ and a $t$, such that the resulting r is the same...Btw, perhaps you could also put your question inside your post instead of only as the title of the thread.
Your post looks a bit out of context now. :o
Haha! It Was a typo I see! I Was trying and trying, i Was like how can $$3+s= 2+s$$

Regards,
$$|\pi\rangle$$
 
I like Serena said:
Hey Raerin! ;)

Let's use a different parameter in both of those line equations.

line 1: r = (3,1,-1) + s(1,2,3)
line 2: r = (2,5,0) + t(1,-1,1)

We're looking for an $s$ and a $t$, such that the resulting r is the same...Btw, perhaps you could also put your question inside your post instead of only as the title of the thread.
Your post looks a bit out of context now. :o

------

So it's not possible for both parameters to be s? Then there's a mistake in the question. I guess I don't need help anymore. Thanks!
 
Raerin said:
------

So it's not possible for both parameters to be s? Then there's a mistake in the question. I guess I don't need help anymore. Thanks!

It's not really a mistake in the question.
The general form of a line equation is $\vec r = \vec a + s \vec d$.
However, when you intersect 2 different lines with such an equation, you have to realize that the parameters $s$ in those 2 line equations are distinct.
 

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