Question

173
28. The harmonic conjugate of (2, 3, 4) w.r.t. the points (3,- 2,2), (6,-17, - 4) is
1) (18/5,- 5,4/5) 2)(11,-16, 2) 3) (1/2, 1/3, 1/4) 4)(0,0,0) ​

Answer 1

Answer:

Step-by-step explanation:

Let P(2,3,4) A(3,-2,2) & B(6,-17,-4)

Let P divides AB in the ratio K:1, then

2=  

K+1

6K+3

​  

 

2K+2=6K+3

K=−1/4

Harmonic conjugate Q divides in the ratio −K:1

i.e  

4

1

​  

:1

Q=[  

1/4+1.1/4+11/4+1

4

1

​  

(6)+3(  

4

1

​  

)(−17)−2(  

4

1

​  

)(−4)+2

​  

]

⇒(  

5

6+12

​  

,  

5

−17−8

​  

,  

5

−4+8

​  

)

⇒(18/5,−5,−4/5)