Given that P(3, 2, -4),Q(5, 4, -6),and R(9, 8 | vedclass

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(A) Let point $Q(5, 4, -6)$ divide the line segment joining points $P(3, 2, -4)$ and $R(9, 8, -10)$ in the ratio $k: 1$.By the section formula,the coo

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$1: 2$

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(A) Let point $Q(5, 4, -6)$ divide the line segment joining points $P(3, 2, -4)$ and $R(9, 8, -10)$ in the ratio $k: 1$.By the section formula,the coordinates of $Q$ are given by:$Q = \left( \frac{k(9) + 3}{k + 1}, \frac{k(8) + 2}{k + 1}, \frac{k(-10) - 4}{k + 1} \right)$Equating the $x$-coordinates:$\frac{9k + 3}{k + 1} = 5$$9k + 3 = 5k + 5$$4k = 2$$k = \frac{2}{4} = \frac{1}{2}$Thus,the ratio $k: 1$ is $\frac{1}{2}: 1$,which is $1: 2$.Therefore,point $Q$ divides $PR$ in the ratio $1: 2$.

Given that $P(3, 2, -4)$,$Q(5, 4, -6)$,and $R(9, 8, -10)$ are collinear. Find the ratio in which $Q$ divides $PR$.

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