The harmonic conjugate of $\left(2,3,4\right)$ with respect to the points $\left(3,-2,2\right),\left(6,-17,-4\right)$ is

The harmonic conjugate of (2,3,4) with respect to the points (3,–2,2),(6,–17,–4) 

The ratio that the point $\left(2,3,4\right)$ with respect to the line segment $A\left(3,-2,2\right),B\left(6,-17,-4\right)$ is $3-2:2-6=-1:4$

The coordinates of a point which divides the line segment joining the points (3,–2,2),(6,–17,–4)  in the ratio $1:4$ internally is $\left(\frac{6+12}{5},\frac{-17-8}{5},\frac{-4+8}{5}\right)=\left(\frac{18}{5},-5,\frac{4}{5}\right)$