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    dot vs. cross

    What is the purpose of the dot product as opposed to the purpose of the cross product?
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    Re: dot vs. cross

    Quote Originally Posted by delgeezee View Post
    What is the purpose of the dot product as opposed to the purpose of the cross product?
    the result of a dot product of two vectors is a scalar ...

    work, a scalar quantity of energy, is the dot product of force and displacement vectors

    W = \vec{F} \cdot \vec{\Delta x}


    the result of a cross product of two vectors is another vector ...

    torque, a vector quantity, is the cross product of radius and force vectors

    \vec{\tau} = \vec{r} \times \vec{F}


    try a google search ... you'll find many more examples and applications.
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    Re: dot vs. cross

    Quote Originally Posted by delgeezee View Post
    What is the purpose of the dot product as opposed to the purpose of the cross product?
    There is a very simple answer and distinction between the two operations.
    The dot product operation maps pairs of vectors to a scalar.
    The cross product operation maps pairs of vectors to a vector.
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