# Equations of a line in three space.

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• Mar 26th 2011, 01:49 PM
darksoulzero
Equations of a line in three space.
The question: A line q is defined be the vector equation [x,y,z]=[4,-3,2] +t[1,8,-3]. Answer the following without technology.

b) determine if line q intersects line r, defined by [x,y,z]=[2,-19,9]+s[4,-5,-9].

I'm not sure how I would do this. I tried setting the parametric equations equal to each other and then solving for t and then subbing into one the original but I was getting a crazy answer. I have no idea how would i do this in 3-space. Any help would be appreciated.
• Mar 26th 2011, 01:57 PM
Plato
Quote:

Originally Posted by darksoulzero
The question: A line q is defined be the vector equation [x,y,z]=[4,-3,2] +t[1,8,-3]. Answer the following without technology.
b) determine if line q intersects line r, defined by [x,y,z]=[2,-19,9]+s[4,-5,-9].

Solve this system $\displaystyle \begin{gathered} ~4 + t = 2 + 4s \hfill \\ - 3 + 8t = 19 - 5s \hfill \\ \end{gathered}$ if the solution also solves $\displaystyle 2-3t=9-9s$ then they intersect.
• Mar 26th 2011, 04:17 PM
darksoulzero
Thanks for the superfast reply. I appreciate your help, but I found out how do it when I googled it.
• Mar 26th 2011, 04:20 PM
Plato
Quote:

Originally Posted by darksoulzero
Thanks for the superfast reply. I appreciate your help, but I found out how do it when I googled it.

Can you googled it on a test?
• Mar 26th 2011, 05:00 PM
darksoulzero
Actually, I found another site similar to this one and it had an example explaining the solution. Also, this is just extra practice and I wanted to try and get the answer on my own so I used google.