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Thread: Unit Cube

  1. #1
    Sep 2008

    Unit Cube

    By locating a unit cube in an appropriate position in the 3-dimensional rectangular coordinate system, determine the acute angle formed by the two diagonals of the cube.
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  2. #2
    MHF Contributor
    skeeter's Avatar
    Jun 2008
    North Texas
    pretty sure this is correct ...

    let one diagonal go from the origin to the point (1,1,1)

    its direction vector is a = <1,1,1>

    let the other diagonal go from (1,0,0) to (0,1,1)

    its direction vector is b = <-1,1,1>

    the dot product of the two direction vectors = 1

    |a| = |b| = $\displaystyle \sqrt{3}$

    $\displaystyle 3\cos{\theta} = 1$

    $\displaystyle \cos{\theta} = \frac{1}{3}$

    $\displaystyle \theta \approx 70.5^{\circ}$
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