The harmonic conjugate of (2,3,4) with respec | vedclass

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(B) Let the points be $A(3,-2,2)$ and $B(6,-17,-4)$. Let $P(2,3,4)$ divide $AB$ in the ratio $k:1$.Using the section formula: $(2,3,4) = \left(\frac{6

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

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(B) Let the points be $A(3,-2,2)$ and $B(6,-17,-4)$. Let $P(2,3,4)$ divide $AB$ in the ratio $k:1$.Using the section formula: $(2,3,4) = \left(\frac{6k+3}{k+1}, \frac{-17k-2}{k+1}, \frac{-4k+2}{k+1}\right)$.Equating the $x$-coordinates: $2 = \frac{6k+3}{k+1}$ $\Rightarrow 2k+2 = 6k+3$ $\Rightarrow -4k = 1$ $\Rightarrow k = -\frac{1}{4}$.The harmonic conjugate $Q$ divides $AB$ in the ratio $-k:1$,which is $\frac{1}{4}:1$ or $1:4$ externally.The coordinates of $Q$ are given by $\left(\frac{1(6)+4(3)}{1+4}, \frac{1(-17)+4(-2)}{1+4}, \frac{1(-4)+4(2)}{1+4}\right)$.Calculating these: $Q = \left(\frac{6+12}{5}, \frac{-17-8}{5}, \frac{-4+8}{5}\right) = \left(\frac{18}{5}, -5, \frac{4}{5}\right)$.

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

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