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Math Help - volume of parallelepiped w/ adjacent edges

  1. #1
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    volume of parallelepiped w/ adjacent edges

    P(2, 0, -1), Q(4, 1, 0), R(3, -1, 1), S(2, -2, 2)

    must find the volume of the parallelepiped with adjacent edges PQ PR and PS.

    I tried setting it up and i still didn't come out with the correct answer of 3

    ...whats confusing me is the amount of points above, there are 4 now, instead of 2, or 3.

    please help.
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  2. #2
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    Hello, rcmango!

    Did you work out the vectors?


    P(2, 0, \text{-}1),\quad Q(4, 1, 0),\quad R(3,\text{-}1, 1),\quad S(2,\text{-}2, 2)

    Find the volume of the parallelepiped with adjacent edges PQ, PR, PS.

    We have: . \begin{array}{ccccc}<br />
\vec u &=& \overrightarrow{PQ} &=& \langle 2,1,1\rangle \\ \vec v &=& \overrightarrow{PR} &=& \langle1,\text{-}1,2\rangle \\ \vec w &=& \overrightarrow{PS} &=& \langle 0,\text{-}2,3\rangle \end{array}


    Then: . \text{Volume} \;=\;\bigg|\vec u \cdot(\vec v \times \vec w)\bigg|

    . . Hence: . V \;=\;\left|\,\begin{bmatrix}2&1&1\\1&\text{-}1&2 \\ 0&\text{-}2&3\end{bmatrix}\,\right|\quad\hdots etc.

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  3. #3
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    okay i see,

    after i calculated PQ PR and PS

    ex: PQ (4-2) + (1-0) + (0+1) 2, 1, 1 ........... and the others....

    i used their cross product for:

    i came out with 2*(2-(-4) - 1(3-0) + 1(-2 - 0)

    everything looks fine except i got a -3,
    thats very close though, probably just another wrong negative somewhere i did.

    thanks for the help.
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  4. #4
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    Quote Originally Posted by rcmango View Post
    ...

    ...whats confusing me is the amount of points above, there are 4 now, instead of 2, or 3.

    please help.
    I've attached a sketch of an parallelepiped.
    Attached Thumbnails Attached Thumbnails volume of parallelepiped w/ adjacent edges-parallelepiped.png  
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  5. #5
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    thanks for the sketch, ya, its much better to see it that way when a paper is not 3d, i appreciate it.
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