Hey, thanks for coming into my thread!

I have a problem involving vectors that I do not know how to start solving.

** Question **
Find the value of k for which the plane

is parallel to the line

.

** Solution **
I know that (k, 4, 2) will be perpendicular to a direction vector on the plane given in the symmetric equation.

Rearranging the symmetric equation gives me:

Which I believe gives me a direction vector on that plane of: (5, 1, -3).

With this information, how can I find the value of k? If I had a second direction vector of the parallel plane I could do a cross product, so is it possible to find that?

Thanks!