1. ## (solved) Lines and Planes

Hi, I'm not sure how to solve the following problem.

Find the parametric equations of a line and a plane that intersects at the point (1,4,-1).

I know how to find the point of intersection of a line and a plane, but I have no idea how to go backwards.

Any help would be appreciated.

Thanks,
Sam

2. I don't think you have given enough information in the question. the line or the plane could be pointing in any direction as long as they pass through the point you have stated. Does it say if the line is normal to the plane for example?

3. Originally Posted by sam314159265
Hi, I'm not sure how to solve the following problem.

Find the parametric equations of a line and a plane that intersects at the point (1,4,-1).

I know how to find the point of intersection of a line and a plane, but I have no idea how to go backwards.

Any help would be appreciated.

Thanks,
Sam
Do you understand that there are an infinite number of planes and lines through any given point?

One answer is to take the line to be x= 1, y= 4, z= t and the plane to be z= -1.

I'm sure you can think up many different answers to this same question!

4. Yeah, I can't believe I didn't think of that... The question makes a lot more sense now. Thanks for the help