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Math Help - Cross product of 3 vectors:

  1. #1
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    Cross product of 3 vectors:

    This is somewhat of a conceptual question that I need resolved as I may have interpreted things wrong:

    When we have two vectors, U and V, taking their cross products (UxV) produces a resultant vector that is orthogonal to both U and V.

    Now if we consider a 3 by 3 matrix in which each row would represent a vector, respectively U, V, W. If we compute the wronskian of the matrix is the resulting vector orthogonal to U, V and W?

    If no could you please clarify why and is there a way to compute a cross product of 3 or more vectors? (possibly by introducing higher dimensions)

    Thank you for the help.
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  2. #2
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    Quote Originally Posted by Armen View Post

    If no could you please clarify why and is there a way to compute a cross product of 3 or more vectors? (possibly by introducing higher dimensions)
    .
    Because the matrix in the first row is composed of the elements of the n-dimensional vector space. The second rule is composed of n-unique elements required for a linear combination and the same for the thirds row. In total you have 3 rows and n elements in each row. In order to compute the determinant we need that n=3. Thus it cannot work for anything more than 3.
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  3. #3
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    Quote Originally Posted by Armen View Post
    This is somewhat of a conceptual question that I need resolved as I may have interpreted things wrong:

    When we have two vectors, U and V, taking their cross products (UxV) produces a resultant vector that is orthogonal to both U and V.

    Now if we consider a 3 by 3 matrix in which each row would represent a vector, respectively U, V, W. If we compute the wronskian of the matrix is the resulting vector orthogonal to U, V and W?
    I don't know what you mean by the Wronskian in this context - it is
    usualy defined for a set of functions.

    If no could you please clarify why and is there a way to compute a cross product of 3 or more vectors? (possibly by introducing higher dimensions)
    Look at the definition of the wedge product in the section on higher dimensions at this link

    RonL
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  4. #4
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    K the links you provided has the information I need thank you for the help.
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