How to find the intersection point between two lines

In summary, the conversation discusses finding the intersection point between two lines, each represented by different equations. The equations have different parameters, and in order for the resulting points to be the same, the parameters must also be different. This leads to the conclusion that there may be a mistake in the question and the parameters in each equation should not both be represented by $s$.
  • #1
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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  • #2
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. :eek:
 
  • #3
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. :eek:
Haha! It Was a typo I see! I Was trying and trying, i Was like how can \(\displaystyle 3+s= 2+s\)

Regards,
\(\displaystyle |\pi\rangle\)
 
  • #4
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. :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!
 
  • #5
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.
 

FAQ: How to find the intersection point between two lines

What is the formula for finding the intersection point between two lines?

The formula for finding the intersection point between two lines is x = (c2 - c1) / (m1 - m2) , where c1 and c2 are the y-intercepts of the two lines, and m1 and m2 are the slopes of the lines.

How do I find the slopes of two lines?

To find the slopes of two lines, use the formula m = (y2 - y1) / (x2 - x1), where x1 and y1 are the coordinates of one point on the line and x2 and y2 are the coordinates of another point on the line.

Can I use this formula to find the intersection point of three or more lines?

No, this formula is specifically for finding the intersection point between two lines. To find the intersection point of three or more lines, you would need to use a different method, such as graphing or using systems of equations.

What if the two lines are parallel?

If the two lines are parallel, they will never intersect and therefore there is no intersection point. In this case, the lines have the same slope and different y-intercepts, or they have the same y-intercept and different slopes.

Is it possible for two lines to have more than one intersection point?

No, two lines can only have one intersection point. If two lines have more than one intersection point, they are not considered to be lines, but rather they are the same line or are coincident lines.

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