Results 1 to 2 of 2

Math Help - Tetrahedron

  1. #1
    Member
    Joined
    May 2006
    Posts
    148
    Thanks
    1

    Tetrahedron

    This is a multi-variable prob.

    We know that a tetrahedron is a solid which has four vertices and has four triangular faces. For every side of a tetrahedron, you can take a vector whose length then is equal to the area of the face and further where its direction is pointing outward perpendicular to the face. Mark these vectors as v_1, v_2, v_3, and v_4.

    1.) Show that v_1 + v_2 + v_3 + v_4 = 0

    2.) Suppose that we have that 3 of the faces of the tetrahedron are perpendicular to each other (now it will look as though it could fit in the very corner of a box. Label these faces A,B,C and the area of the 4th face as D. Prove that D^2 = A^2 + B^2 + C^2

    HINTS: you will need to use vector products - also, you may want to use a coordinate system such that one vertex will lie at the origin (and then from there consider edges as vectors)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    May 2006
    Posts
    148
    Thanks
    1
    This is apparently our hardest problem for this assignment. I'd appreciate it if someone could point me in the right direction of how to solve these.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. tetrahedron,
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: July 14th 2009, 02:09 AM
  2. tetrahedron
    Posted in the Geometry Forum
    Replies: 1
    Last Post: January 8th 2009, 01:35 PM
  3. tetrahedron 2
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 29th 2008, 08:21 PM
  4. tetrahedron
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 29th 2008, 03:26 PM
  5. Tetrahedron
    Posted in the Geometry Forum
    Replies: 4
    Last Post: March 21st 2008, 02:07 AM

Search Tags


/mathhelpforum @mathhelpforum