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[SOLVED] How to find the intersection point between two lines

Raerin

Member
Oct 7, 2013
46
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)
 
Last edited by a moderator:

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,851
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. :eek:
 

Petrus

Well-known member
Feb 21, 2013
739
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. :eek:
Haha! It Was a typo I see!! I Was trying and trying, i Was like how can \(\displaystyle 3+s= 2+s\)

Regards,
\(\displaystyle |\pi\rangle\)
 

Raerin

Member
Oct 7, 2013
46
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. :eek:
------

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!
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,851
------

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.