First slide

Introduction to 3-D Geometry

Question

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

Very Easy

A

$(11, - 16, 2)$
B

$(\frac{18}{5}, - 5, \frac{4}{5})$
C

$(\frac{18}{5}, 5, \frac{4}{5})$
D

$(- \frac{18}{5}, - 5, \frac{4}{5})$

Solution

The point $(2, 3, 4)$ divides the line segment joining the points $(3, - 2, 2)$ , $(6, - 17, - 4)$ in the ratio $3 - 2 : 2 - 6 = 1 : - 4$
The hormonic conjugate of point $(2, 3, 4)$ with respect to the line segment joining the points $(3, - 2, 2)$ , $(6, - 17, - 4)$ divides the line segment in the ratio internally
Required the point is $(\frac{6 + 12}{5}, \frac{- 17 - 8}{5}, \frac{- 4 + 8}{5}) = (\frac{18}{5}, - 5, \frac{4}{5})$

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