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Math Help - scalar triple product, coplanar vectors.

  1. #1
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    scalar triple product, coplanar vectors.

    a = 2i+ 3j +k,
    b = i - j,
    c = 7i + 3j +2k

    must use the scalar triple product to conclude that they are coplanar.

    i tried this using a *(b x c)

    i also said b was b = i - j +0k ??

    so i came out with

    2(-2-0) + 3(2-0) + 1(3 - -7)

    for -4 +6 + 10

    don't think this is correct though, i think they need to be 0.

    thanks for any help.
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  2. #2
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    Hello, rcmango!

    You dropped a minus-sign . . .


    \begin{array}{c}a \:=\:2i+ 3j +k \\<br />
b \:=\: i - j \\ c \:=\: 7i + 3j +2k\end{array}

    Use the scalar triple product to conclude that they are coplanar.
    We have: . \begin{array}{c}a \;=\:\langle2,3,1\rangle \\ b \:=\:\langle1,\text{-}1,0\rangle \\ c \:=\:\langle 7,3,2\rangle \end{array}

    . . . . . . . . . {\color{red}^{+\quad-\quad+} }
    a\cdot(b\times c) \;=\; \begin{vmatrix}2&3&1 \\ 1&\text{-}1&0 \\ 7&3&2\end{vmatrix}\;=\;2(\text{-}2-0) \:{\color{red}-}\:3(2-0) \:+\: 1(3-[\text{-}7])<br /> <br /> <br /> <br />

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  3. #3
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    thanks, ya i'm finding out its really easy to miss signs in these types of problems.
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