The value of K so that the system of equations $x+ky+3z=0,3x+ky-2z=0,2x+3y-4z=0$have non zero solution then

$The condition for a homogeneous system to have a non-zero solution is \Delta =0$

$\begin{array}{l}\Rightarrow \left|\begin{array}{ccc}1& k& 3\\ 3& k& -2\\ 2& 3& -4\end{array}\right|=0\\ \Rightarrow 1\left(-4k+6\right)-k\left(-12+4\right)+3\left(9-2k\right)=0\\ \Rightarrow -4k+6+8k+27-6k=0\\ \Rightarrow -2k=-33\Rightarrow k=\frac{33}{2}\\ \Rightarrow k=16.5\end{array}$