Explore BrainMass
Share

Explore BrainMass

    Vectors : Planes, Points, Cross Product and Dot Product

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

    (1) a. Find the (vector) equation of the plane passing through the points (1,2,-2),
    (-1,1,-9), (2,-2,-12).

    b. Find the (vector) equation of the plane containing (1,2,-1) and perpendicular to
    (3,-1,2).

    (2) Suppose a, b, c are non zero vectors.

    a. Explain why (a x b) x (a x c) is in the direction of a.

    b. Show that (a x b) x (a x c ) = ( a . b x c) a.

    c. Show that a x b . (b x c) x (c x a) = (a . b x c)²

    © BrainMass Inc. brainmass.com October 9, 2019, 3:45 pm ad1c9bdddf
    https://brainmass.com/math/vector-calculus/vectors-planes-points-cross-product-and-dot-product-12548

    Attachments

    Solution Summary

    A vector equation of a plane is found. Dot and Cross products are calculated. The solution is detailed.

    $2.19