# 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 $\displaystyle \frac{x+3}{2} = \frac{y-2}{3} = \frac{z-1}{2}$ and is parallel to the line $\displaystyle r = (1+3t)i + (2t)j + (4-t)k$

Solution
I don't understand what the $\displaystyle r = (1+3t)i + (2t)j + (4-t)k$ 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 $\displaystyle \frac{x+3}{2} = \frac{y-2}{3} = \frac{z-1}{2}$ and is parallel to the line $\displaystyle r = (1+3t)i + (2t)j + (4-t)k$
From $\displaystyle r = (1+3t)i + (2t)j + (4-t)k$ we get $\displaystyle \ell (t) = \left\{ {\begin{array}{l} {x = 1 + 3t} \\ {y = ~~~2t} \\ {z = 4 - t} \\ \end{array} } \right.$
You want the plane that contains $\displaystyle (-3,2,1)$ with normal $\displaystyle <3,2,-1>\times <2,3,2>$.