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What figure do these 3D vectors make?

  1. Mar 12, 2013 #1
    1. The problem statement, all variables and given/known data
    The vertices of a figure are given by A(-8, 4, -2), B(-6, 3, 5), and C(-10, 5, -9). What type of figure is ABC? Why?

    2. Relevant equations
    pythagorean theorem: |AB|=√(x^2+y^2+z^2)

    3. The attempt at a solution
    I first found the vector AB, BC, and CA by subtracting the components of the vectors.
    Then I calculation the magnitude of |AB|, |BC|, and |CA| using the pythagorean theorem.
    I got this |AB|=3√6 |BC|=6√6 and |CA|=3√6
    According to my calculation, point A is on the line connecting points B and C, so the 3 points are collinear and form a line.

    But the answer seems wrong since they are asking for a type of a figure.
  2. jcsd
  3. Mar 12, 2013 #2
    The vectors are indeed linearly interdependent, your conclusion is correct.
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