Explore BrainMass
Share

Explore BrainMass

    Altitude of a perallelepiped

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Find the altitude of a parallelepiped determined by vectors A, B, and C if the base is taken to be the parallelogram determined by A and B and
    A=i+j+k
    B=2i+4j-k
    C=i+j+3k.

    © BrainMass Inc. brainmass.com October 10, 2019, 1:34 am ad1c9bdddf
    https://brainmass.com/math/geometry-and-topology/altitude-perallelepiped-340069

    Solution Preview

    The altitude of such a parallelepiped is precisely the length of the orthogonal projection of C onto the cross-product of A and B.
    It can be readily seen from a picture. The cross-product A X B is perpendicular to both A and B, and if we project C onto it, ...

    Solution Summary

    The altitude of a parallelepiped determined by three vectors is calculated.

    $2.19