Parametric Vector Problem

1. Mar 14, 2014

gomess

1. The problem statement, all variables and given/known data

2. Relevant equations
(x,y,z)=(x0,y0,z0) + t(m1,m2,m3)

3. The attempt at a solution
So at first I thought that since vector P1P2 is at right angles to both lines, both lines must be parallel. Quickly dismissed this idea since their direction vectors are not multiples of one another. Then I thought P1P2 could be the cross product of both direction vectors... crossed both vectors and got P1P2=(-1,3,1). Not sure if that's the right approach, and not sure what to do from here. Any help would be great!

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Last edited: Mar 14, 2014
2. Mar 14, 2014

SammyS

Staff Emeritus
Posting the image will make it more likely that your question will get attention:

I haven't worked through the problem, but it seems to me that the dot product (scalar product) may work better.

3. Mar 14, 2014

gomess

I'll try using the scalar product and see where it gets me.
Edit: No progress. I figured that since P1 lies on L1, some value of 't' would take me to P1 and from there, vector P1P2 would take me to P2 (assuming P1P2 is the cross product of the direction vectors).

Last edited: Mar 14, 2014
4. Mar 14, 2014

SammyS

Staff Emeritus
Oh! Yes, that should work for the direction of $\displaystyle\vec{P_1P_2} \ .\$ You were correct about the result of <-1, 3, 1>