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Math Help - Vector question

  1. #1
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    Vector question

    3. Use cross product to find the sine of the angle between the vectors

    u (2, 3, -6)

    v (2, 3, 6)
    Last edited by daphnewoon; October 24th 2009 at 09:11 AM.
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  2. #2
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    Hello, daphnewoon!

    1. Giiven the points: . O:(0, 0, 0),\;P:(2, 6, \text{-}1),\;Q:(1, 1, 1),\; R(4, 6, 2)

    Find a vector \vec{n} that is perpendicular to both \overrightarrow{PQ} and \overrightarrow{OR}.

    We have: . \begin{array}{ccc}\overrightarrow{PQ} &=& \langle \text{-}1,\text{-}5,2\rangle \\ \overrightarrow{OR} &=& \langle 4,6,2\rangle \end{array}

    Then: . \vec{n} \;=\;\overrightarrow{PQ} \times \overrightarrow{OR} \;=\;\left|\begin{array}{ccc}i&j&k \\ \text{-}1& \text{-}5 & 2\\4 & 6 & 2\end{array}\right| \;=\;\text{-}22i + 10j + 14k \;=\;\langle 11,\text{-}5,\text{-}7\rangle

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  3. #3
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    Thanks=)

    THank you, soroban for replying.
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