Originally Posted by

**sobering** Hey emakarov and Plato, thanks for your answers. After reading both your posts the solution immediately became obvious. I suppose I was overthinking the question.

I didn't want to post the actual question because I wanted to understand the process, and not just receive an answer. The vectors were $\displaystyle <4, 2, 7>$ and $\displaystyle <2, 1, k>$.

For the orthogonal aspect of the question, here's my solution:

$\displaystyle <4, 2, 7> \cdot <2, 1, k> = 0$

$\displaystyle = 4(2) + 2(1) + 7k = 0$

$\displaystyle k = -10$

Thanks again for all your help.