If \(\mathrm{k}_{\mathrm{i}}\) are possible values of \(\mathrm{k}\) for which lines \(\mathrm{k} x+2 y+2=0,2 x+\mathrm{k} y+3=0\) and \(3 x+3 y+\mathrm{k}=0\) are concurrent, then \(\sum \mathrm{k}_{\mathrm{i}}\) has the value

If three lines \(\mathrm{a}_1 x+\mathrm{b}_1 y+\mathrm{c}_1=0\), \(\mathrm{a}_2+\mathrm{b}_2 y+\mathrm{c}_2=0\) and \(\mathrm{a}_3 x+\mathrm{b}_3 y+\mathrm{c}_3=0\) are
\(
\begin{aligned}
& \text { concurrent, then }\left|\begin{array}{lll}
a_1 & b_1 & c_1 \\
a_2 & b_2 & c_2 \\
a_3 & b_3 & c_3
\end{array}\right|=0 \\
& \Rightarrow\left|\begin{array}{lll}
k & 2 & 2 \\
2 & k & 3 \\
3 & 3 & k
\end{array}\right|=0 \\
& \Rightarrow k^2\left(k^2-9\right)-2(2 k-9)+2(6-3 k)=0 \\
& \Rightarrow k^3-9 k-4 k+18+12-6 k=0 \\
& \Rightarrow k^3-19 k+30=0 \\
& \Rightarrow(k-2)\left(k^2 42 k-15\right)=0 \\
& \Rightarrow(k-2)(k+5)(k-3)=0 \\
& \Rightarrow k_1=2, k_2=-5 \text { and } k_3=3 \\
& \Rightarrow \sum k_i=0
\end{aligned}
\)