Let we points $\mathrm{P}(2,3,4), \mathrm{A}(3,-2,2)$ and $\mathrm{B}(6,-17,-4)$. and $\mathrm{P}$ divides $\mathrm{AB}$ in the ratio $k: 1$ then
$\begin{aligned}
& (2,3,4)=\left(\frac{6 k+3}{k+1}, \frac{-17 k-2}{k+1}, \frac{-4 k+2}{k+1}\right) \\
& 2=\frac{6 k+3}{k+1} \\
& \Rightarrow \quad 2 k+2=6 k+3 \\
& \Rightarrow-4 k=1 \Rightarrow k=-\frac{1}{4}
\end{aligned}$
Harmonic conjugate $\mathrm{Q}$ divides in the ratio $-k: 1$, So Ratio will be $\frac{1}{4}: 1$
$\therefore \quad$ Coordinates of $\mathrm{Q}$
$\begin{aligned}
& =\left(\frac{\frac{1}{4}(6)+3}{\frac{1}{4}+1}, \frac{\frac{1}{4}(-17)-2}{\frac{1}{4}+1}, \frac{\frac{1}{4}(-4)+2}{\frac{1}{4}+1}\right) \\
& =\left(\frac{6+12}{5}, \frac{-17-8}{5}, \frac{-4+8}{5}\right) \\
& =\left(\frac{18}{5},-5 \frac{4}{5}\right)
\end{aligned}$