If the points A(9, 8, -10),B(3, 2, -4) and C( | vedclass

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(A) Let the point $C(5, 4, -6)$ divide the line segment joining $A(9, 8, -10)$ and $B(3, 2, -4)$ in the ratio $k:1$.Using the section formula,the coor

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$2:1$

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(A) Let the point $C(5, 4, -6)$ divide the line segment joining $A(9, 8, -10)$ and $B(3, 2, -4)$ in the ratio $k:1$.Using the section formula,the coordinates of $C$ are given by:$C = \left( \frac{3k + 9}{k + 1}, \frac{2k + 8}{k + 1}, \frac{-4k - 10}{k + 1} \right)$Equating the $x$-coordinate to $5$:$\frac{3k + 9}{k + 1} = 5$$3k + 9 = 5k + 5$$4 = 2k$$k = 2$Thus,the ratio $k:1$ is $2:1$.Therefore,the point $C$ divides the line segment $AB$ in the ratio $2:1$.

If the points $A(9, 8, -10)$,$B(3, 2, -4)$ and $C(5, 4, -6)$ are collinear,then the point $C$ divides the line segment $AB$ in the ratio:

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