I need to find a vector that is perpendicular to the vectors $[2, 3, 2]$ and $[4, 9, 5]$. I have not been taught the method with cross-products using matrices so I cannot use that method while solving the problem.
I was thinking of using systems of equations to solve this problem and find the line that is the intersection of the two planes with the given normal vectors.
$$2x + 3y + 2z =0$$ $$4x+ 9y+5z=0$$
I used elimination method to get $3y + z = 0$. I know that if I choose that $y = 1$, then $z = -3$. I was thinking that since I eliminated $x$, then its value will be $0$. So I thought that the vector would be $[0, 1, -3]$, however, after computing the dot products I know that that vector is incorrect. Any help will be greatly appreciated.