Results 1 to 2 of 2

Math Help - Vector Proofs

  1. #1
    Newbie
    Joined
    Oct 2005
    Posts
    3

    Vector Proofs

    1) Prove that the line segments of a tetrahedron that join the vertices to the centroids of the opposite faces are concurrent and intersect each other in the ratio of 3:1.

    2)Prove that if the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jun 2005
    Posts
    295
    Awards
    1
    If the position vectors of the four vertices are a,b,c,d then the centroid of the face containing a,b,c is (a+b+c)/3 and the line joining it to the opposite vertex d is the set td + (1-t)(a+b+c)/3 for any value of t. Find a value of t which gives a point symmetric in a,b,c,d.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Vector proofs for triangles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: June 30th 2010, 12:24 AM
  2. vector space proofs
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: October 18th 2009, 04:27 AM
  3. vector space proofs
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 4th 2009, 03:36 PM
  4. Vector Proofs
    Posted in the Geometry Forum
    Replies: 4
    Last Post: December 7th 2006, 11:41 AM
  5. Need some help, vector proofs
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 21st 2006, 10:17 AM

Search Tags


/mathhelpforum @mathhelpforum