# Thread: Plane equation given parallel lines

1. ## Plane equation given parallel lines

Hi

I'm not to sure how to approach this could someone help me out?

2 parallel lines:
L1=(1,0,0) + s(1,-1,-4)
L2=(2,4,0) + t(1,-1,-4)

Find a vector parametric equation of the plane the contains both these parallel lines.

edit: I'm thinking get another direction vector from (2,4,0)-(1,0,0)..is this correct?

2. Originally Posted by Sam1111
Hi

I'm not to sure how to approach this could someone help me out?

2 parallel lines:
L1=(1,0,0) + s(1,-1,-4)
L2=(2,4,0) + t(1,-1,-4)

Find a vector parametric equation of the plane the contains both these parallel lines.
Find the vector that starts at $\displaystyle (1,0,0)$ and ends at $\displaystyle (2,4,0)$. Then find the cross product between this vector and $\displaystyle \left<1,-1,4\right>$. This will generate a normal vector to the plane that contains both lines.

From there, use any point to help you generate the equation for the plane.

Can you take it from here?

3. So I can get the normal and then cross product that with another point to get another direction vector?

So i could do (-16,4,-5)X(1,0,0)? and get (0,-5,-4) as the second direction vector?