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Math Help - Lines and Planes Help!

  1. #1
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    Post Lines and Planes Help!

    A(1,2,k) lies on the plane x + 2y - 2z = 8. Find:

    a) the value of k.
    b) the coordinates of B such that AB is normal to the plane and 6 units from it.
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  2. #2
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    Well a) according to me would be (assuming in the place of k there should the z axis coordinate, so then z=k) 1 + 2*2 - 2z = 8 => 1 + 4 - 2z = 8 => 2z = 5 - 8 => 2z = -3 /:2 => z = -1.5
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  3. #3
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    The part b) is a good bit more difficult.

    We need to find a value of t so that \overrightarrow {AB}  = t\left\langle {1,2, - 2} \right\rangle \;\& \,\left\| {t\left\langle {1,2, - 2} \right\rangle } \right\| = 6

    Note there are two such points for B.
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