AP EAMCET Engineering 2018 Apr 23 Shift 2 Paper

Let the point P(−9,12,−15) divides the line joining A=(1,−2,3) and B=(−4,5,−6) in ratio λ : 1 then,
−9=

−4λ+1

λ+1

,λ=−2
So, the harmonic conjugate of point P with respect to the line segment AB will divide the line segment AB internally in ratio 2:1, so, point will be,
(

−8+1

3

,

10−2

3

,

−12+3

3

) =(−

7

3

,

8

3

,−3)