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Math Help - Find the cartesian equation of a plane that is parallel to i + j + k - Confused!

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    Find the cartesian equation of a plane that is parallel to i + j + k - Confused!

    Hey guys! My class never learned how to do Cartesian coordinates, so I am rather lost as to how to do this question!

    Question
    Find the Cartesian equation o the plane that contains the line  \frac{x+3}{2} = \frac{y-2}{3} = \frac{z-1}{2} and is parallel to the line  r = (1+3t)i + (2t)j + (4-t)k

    Solution
    I don't understand what the  r = (1+3t)i + (2t)j + (4-t)k means. Can I use this and put it into vector or parametric form? If I knew how to do that I could find the solution to the question. Especially vector form.

    Thank you!
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  2. #2
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    Quote Originally Posted by Kakariki View Post
    Find the Cartesian equation o the plane that contains the line  \frac{x+3}{2} = \frac{y-2}{3} = \frac{z-1}{2} and is parallel to the line  r = (1+3t)i + (2t)j + (4-t)k
    From  r = (1+3t)i + (2t)j + (4-t)k we get <br />
\ell (t) = \left\{ {\begin{array}{l}<br />
   {x = 1 + 3t}  \\<br />
   {y = ~~~2t}  \\<br />
   {z = 4 - t}  \\ \end{array} } \right.
    You want the plane that contains (-3,2,1) with normal <3,2,-1>\times <2,3,2>.
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