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

1. ## 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!

2. Originally Posted by Kakariki
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 $
\ell (t) = \left\{ {\begin{array}{l}
{x = 1 + 3t} \\
{y = ~~~2t} \\
{z = 4 - t} \\ \end{array} } \right.$

You want the plane that contains $(-3,2,1)$ with normal $<3,2,-1>\times <2,3,2>$.