1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Putting z in terms of x and y

  1. Oct 19, 2004 #1
    Minimizing Volume

    If I have a linear plane that cuts through the first octant so that there is a z, y, and x intercept so that you have a triangular face in the octant, is there any way I can put z in terms of x and y? Here's what I'm trying to do

    I'm trying to find some linear plane that cuts off the smallest volume in the first octant. The plane must pass through a specific point (let's say it's (2,3,4). I figured since V = Bh and h will stay the same (distance from origin to the point), you will want to minimize the area of the triangular face. So I set each vertice of the triangle as (x,0,0), (0,y,0), and (0,0,z) and take half the cross product of the two vectors <x,0,-z> and <0,y,-z>. But I only know how to find the minimum for only two variables. Is there anyway I could put z in terms of x and y?

    I know there is the eq. ax+by+cz+d=0 but I don't see how it would relate to what I'm trying to do right now (finding the mimimum area of the triangular face) and if there is a connection, I don't see it. I think I just use it later on to find the equation for the plane, but right now I'm trying to find the x,y, and z intercepts of the plane..

    Or am I just approaching this problem in the wrong way?

    Thanks for the help
     
    Last edited: Oct 19, 2004
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted