# Thread: To find a point on a line (in euclidian space) given it intersects two other lines?

1. ## To find a point on a line (in euclidian space) given it intersects two other lines?

so given that a line is parallel to the x axis (so the direction vector = lambda( 1i + 0j + 0k)

and given it intersects two other KNOWN lines, how can you go about fiinding the equation of that line (that intersects the two lines).

technically all you need now is a know point (because we already have the direction vector), but i can't find out how!

help much appreciated thanks!!

2. Originally Posted by Yehia
so given that a line is parallel to the x axis (so the direction vector = lambda( 1i + 0j + 0k)
and given it intersects two other KNOWN lines, how can you go about fiinding the equation of that line (that intersects the two lines).
technically all you need now is a know point (because we already have the direction vector), but i can't find out how!
I think that is just far too vague to answer.
Can you post an actual problem?

3. Originally Posted by Plato
I think that is just far too vague to answer.
Can you post an actual problem?
Ok sure,

A line (in 3D euclidian space) that we are interested in finding is parallel to the x-axis.

Furthermore, it cuts the lines d and l

d = (2 + ß)i + (2 + 2ß)j + (2ß)k

and l = (2)i + (3λ)j + (2λ)k

(where λ and ß are parameters)

so how can you find the equation of that line? all i know now is that it has the direction vector (λi + 0j + 0k)...

4. Originally Posted by Yehia
A line (in 3D euclidian space) that we are interested in finding is parallel to the x-axis.
Furthermore, it cuts the lines d and l
d = (2 + ß)i + (2 + 2ß)j + (2ß)k
and l = (2)i + (3λ)j + (2λ)k (where λ and ß are parameters)
so how can you find the equation of that line? all i know now is that it has the direction vector (λi + 0j + 0k)...
I may not understand your question.
But I do not think that such a line can exists.