Determine a plan detailing on how you would find the value(s) of k, if any, that would make the planes $\displaystyle kx + 2ky + 5z - 6 = 0$ and $\displaystyle -x + (k - 1)y - 7z - 9 = 0$ perpendicular. Implement your plan and solve for k.

I tried use the dot product to solve this problem, but it just got messy and got a headache ...

Is there an easier way to solve for it and if so, please show in full steps?

Answer:

$\displaystyle k = 5$

$\displaystyle k = - \frac{7}{2}$