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    The equation of a plane

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    Part I:

    <(u x v), u> is greater than 0 for all vectors u and v in R^3.

    Part II:

    The equation of the plane through the origin determined by two vectors u and v in R^3 is <(u x v), x> = 0.

    Are these statements true or false and please explain why.

    © BrainMass Inc. brainmass.com October 10, 2019, 2:23 am ad1c9bdddf
    https://brainmass.com/math/vector-calculus/equation-plane-375513

    Solution Preview

    I. The statement is false. The cross-product u x v is perpendicular to both u and v, and so the dot product of (u x v) and u is zero for all u and v from R^3.

    II. This statement is true. The equation of a plane can be derived as follows: ...

    Solution Summary

    This solution thoroughly demonstrates the equation of a plane.

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