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

Step-by-step solution

Let A=(3,-2,2) aligned & B=(6,-17,-4) & P=(2,3,4) aligned Let P divides A B in the ratio of m: n . gathered P= [ m x₂+n x₁ m+n , m y₂+n y₁ m+n , m z₂+n z₁ m+n ] (2,3,4)= [ m(6)+n(3) m+n , m(-17)+n(-2) m+n , . (2,3,4)= [ 6 m(-4)+n(2) m+n ] 6 m+3 n m+n =2 6 m+3 n=2 m+2 n 4 m=-n m n =- 1 4 m: n=-1: 4 gathered We know that, If point P divides a line segment in the ratio of m: n , then its harmonic conjugate will divide same segment in the ratio of -m: n Required ratio =-m: n=1: 4 Required harmonic conjugate aligned & =