AP EAMCET Engineering 22 Sep 2020 Shift 2 Paper

Let A=(3,−2,2)
B=(6,−17,−4)
P=(2,3,4)
Let P divides AB in the ratio of m:n
‌

6m+3n

m+n

=2
6m+3n=2m+2n
4m=−n
‌

m

n

=−‌

1

4

∴‌‌m:n=−1:4
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