Let A(1, –1, 3), B(2, 3, 5) is divided by P in the ratio 3:4 internally then harmonic conjugate of P w.r.t. to A, B is

Given that the line segment joining  the points $A\left(1,-1,3\right),B\left(2,3,5\right)$ is divided by $P$ in the ratio $3:4$ internally 

The harmonic conjugate of $P$ w.r.t. to $A,B$ divides the line segment joining the above two points $3:4$ externally. 

Hence the coordinates of Harmonic conjugate of the point $P$ are $\left(\frac{6-4}{-1},\frac{9+4}{-1},\frac{15-12}{-1}\right)=\left(-2,-13,-3\right)$