I am trying to find values for a and b for the following set of vectors:
$\left(\left[\begin{matrix} 1\\2\\3\end{matrix}\right],\left[\begin{matrix} 4\\1\\-2\end{matrix}\right], \left[\begin{matrix} a\\b\\3\end{matrix}\right]\right) = 0$
I know the idea is that, if I take the dot product of all the column vectors in the above vector space, I should end up with zero. But I am not sure how to get started solving for a and b, such that the below set of vectors is orthogonal. A hint as to how to get started?