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Math Help - Finding/determining equidistant point between vectors.

  1. #1
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    Finding/determining equidistant point between vectors.

    So here's the problem:

    "Let A = (0,0,0), B = (2,0,0), C = (1, sqrt(3), 0), and D = (1, 1/sqrt(3), 2*sqrt(2/3).

    a) Show that A, B, C, D are all the same distance from each other.
    b) Find the point P = (x, y, z) which is equivalent from A, B, C, and D by setting up and solving three equations in x, y, and z."

    I'm not sure how to go about solving this problem. For a, can I simply find the length of each vector and compare them?
    And for b, I honestly have no idea. Help?
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  2. #2
    Member rtblue's Avatar
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    Birmingham, Alabama.
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    Here is the distance formula for points in 3D. That should solve part A for you.

    Use that same formula for part B. In terms of x,y, and z set up a system of equations using the distance formula, with respect to points A,B,C, and D.
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