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Math Help - vector questions

  1. #1
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    vector questions

    If 1) a=i+j+k \ \mbox{find}\ b \ \mbox{if}\ a\cdot\mbox{b}=8\ \mbox{and}\ a\times\mbox{b}=6i-7j+k

    2)If a = i + j + k, explain why it is not possible that a x b = i - j + 2k. Show that if a x b = xi + yj + zk, then x + y +z = 0

    THanks
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  2. #2
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    Quote Originally Posted by ashes View Post
    If 1) a=i+j+k \ \mbox{find}\ b \ \mbox{if}\ a\cdot\mbox{b}=8\ \mbox{and}\ a\times\mbox{b}=6i-7j+k

    ...
    Let b = (x, y, z) then you know:

    [1]: (1, 1, 1) * (x, y, z) = x + y + z = 8

    [2]: (1, 1, 1) \times (x, y, z) = (6, -7, 1)

    #[2] will yield: (z-y, x-z, y-x) = (6, -7, 1)

    You'll get a system of simultaneous equations:

    \left|\begin{array}{lcr}z-y&=&6 \\ x-z&=& -7 \\y-x&=&1 \\x+y+z&=&8\end{array} \right.

    Solve for (x, y, z). I've got: (x, y, z) = (0, 1, 7)
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