Originally Posted by

**Kakariki** 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 $\displaystyle kx + 4y + 2z - 6 = 0 $ is parallel to the line $\displaystyle \frac{x - 3}{5} = \frac{y}{1} = \frac {z}{-3} $.

** 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:

$\displaystyle x = 5t + 3 $

$\displaystyle y = t $

$\displaystyle z = -3t $

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!