area question?

Find the volume of the parallelepiped with one vertex at (−3,−1,5), and adjacent vertices at (1,−2,−2), (−2,−1,0), and (−3,1,−1). 

How can I answer this question using the determinant of a 3x3 matrix?

1 Answer

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  • 1 month ago

    The volume is |(aXb) "dot" c|, where

    a = <4, -1, -7>,

    b = <1, 0, -5>,

    c = <0, 2, -6>.

    The cross product aXb is

    <5 + 0, -7+20, 0+1> = <5, 13, 1>.

    Dotting that with "c" gives 0 + 26 - 6 = 20.

    You should double check my arithmetic, but I say the answer is 20.

    • Exp1 month agoReport

      That was correct.  One question, when you did aXb how did you get 0+1 for the k component?

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