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!