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Math Help - three vectors are linearly independent

  1. #1
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    three vectors are linearly independent

    I am suppose to use the standard volume interpretation of the scalar triple product a dot b crossed with c


    where a, b and c are my vectors to support that these vecors are independent. I realize that their determinant matrix is not zero and that is what defines independence, but I do not know what the question is asking me to do!!! Any guidance would be much appreciated. Frostking
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by Frostking View Post
    I am suppose to use the standard volume interpretation of the scalar triple product a dot b crossed with c


    where a, b and c are my vectors to support that these vecors are independent. I realize that their determinant matrix is not zero and that is what defines independence, but I do not know what the question is asking me to do!!! Any guidance would be much appreciated. Frostking
    If a\cdot(b\times c)=0, then the volume of the parallelepiped formed by the three vectors is 0. But that means that a, b, and c all lie in the same plane and are therefore not linearly independent. (Since a plane is spanned by exactly two vectors, a third vector in the plane must be a linear combination of the other two.)
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