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Math Help - line vector

  1. #1
    Faz
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    line vector

    Find equation of the line containing the given point (5,3,4) and parallel to the vector
    -> -> ->
    2 i + 5 j - 8 k
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  2. #2
    Senior Member vincisonfire's Avatar
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    x=2t+5
    y=5t+3
    z=-8t+4
    -\infty \leq t \leq \infty
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  3. #3
    Faz
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    plse assist

    can show me the working i still don't understand??
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  4. #4
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    Quote Originally Posted by Faz View Post
    can show me the working i still don't understand??
    I fear that one either understands or not: it is that simple.
    \begin{gathered}<br />
\ell :\left\langle {5,3,4} \right\rangle + t\left\langle {2,5, - 8} \right\rangle \hfill \\<br />
\ell :\left\langle {5 + 2t,3 + 5t,4 - 8t} \right\rangle \hfill \\ <br />
\end{gathered}
    \ell :\left\{ \begin{gathered}<br />
x = 5 + 2t \hfill \\<br />
y = 3 + 5t \hfill \\<br />
z = 4 - 8t \hfill \\ <br />
\end{gathered} \right.
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  5. #5
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    Hello, Faz!

    You're expected to know the formulas for this problem.


    Find equation of the line containing the given point (5,3,4)
    and parallel to the vector \vec c \:=\:2\vec i + 5\vec j - 8\vec k

    Parametric equations: . \begin{array}{ccc}x &=&5+2t \\ y&=&3+5t \\ z&=&4-8t \end{array}


    Symmetric equation: . \frac{x-5}{2} \:=\:\frac{y-3}{5} \:=\:\frac{z-4}{-8}

    Last edited by mr fantastic; December 7th 2008 at 03:31 AM. Reason: No edit - I just wanted to flag this post as a (moved) reply to questions that had been re-posted after replies were given
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  6. #6
    Senior Member vincisonfire's Avatar
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    You set your x,y,z so that they start at (5,3,4). These are some kind of x,y,z-intercept if you want.
    Then you know that in time t, x is going to increase by 2, y is going to increase by 5 and z is going to increase by -8.
    You thus have "3 equations".
    <br />
\ell :\left\{ \begin{gathered}<br />
x = 5 + 2t \hfill \\<br />
y = 3 + 5t \hfill \\<br />
z = 4 - 8t \hfill \\ <br />
\end{gathered} \right.<br />
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