# Finding a plane that contains 2 lines.

## Homework Statement

I have 2 parametric equations of 2 lines. I want to find if there is a plane that contains both, if any, and find the equation.

## The Attempt at a Solution

so just thinking about it, I figure that a plane would contain both lines only if they intersect. Is that right?
if so, my second problem is finding the equation of the said plane. So for both the lines, do I plug in any value of t in the parametric equations to find 2 vectors, take the cross product to find a normal and use that for my equation?

Mark44
Mentor

## Homework Statement

I have 2 parametric equations of 2 lines. I want to find if there is a plane that contains both, if any, and find the equation.

## The Attempt at a Solution

so just thinking about it, I figure that a plane would contain both lines only if they intersect. Is that right?
No, you could have two parallel lines, and they would determine a plane. The only way two lines would not determine a plane is if they are skew lines - lines that aren't parallel and that don't intersect.

I'm assuming that you're working in three dimensions.
if so, my second problem is finding the equation of the said plane. So for both the lines, do I plug in any value of t in the parametric equations to find 2 vectors, take the cross product to find a normal and use that for my equation?

No, you could have two parallel lines, and they would determine a plane. The only way two lines would not determine a plane is if they are skew lines - lines that aren't parallel and that don't intersect.

I'm assuming that you're working in three dimensions.
thanks. Totally forgot about the parallel case. So I set my parametric equations equal to each other and found an intersection point. Yes this is in 3 dimensions