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Math Help - [SOLVED] Vector Algebra (prove line lies on the plane)

  1. #1
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    [SOLVED] Vector Algebra (prove line lies on the plane)

    hey there...
    need guidance to solve my vector problem here.. =)
    Let Rd = (a)i + (6)j + (1)k be the position vector of point D.
    Determine the value of a so that D lies in the plane ABC
    ABC plane => x + 6y -8z = 5
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  2. #2
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    In order that

    \mathbf{R}_D=a\mathbf{i}+6\mathbf{j}+\mathbf{k}

    point from the origin to a point on

    x+6y-8z=5,

    it is enough that the components of \mathbf{R}_D satisfy the equation that defines the plane: that is, that

    a+6\cdot 6-8\cdot 1=5.
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  3. #3
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    what is the general equation for
    (a x 1) + (6 x 6) + (8 x 1) = 5 ?
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  4. #4
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    Carrying out the multiplication, we obtain

    \begin{aligned}<br />
a+36-8&=5\\<br />
a+28&=5.\end{aligned}

    Now, we must solve for a. Hint: we may do something to both sides of the equation.
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  5. #5
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    a = -23?
    am i correct?
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  6. #6
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    You are correct.
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  7. #7
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    thanks Scott!! =)
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