The ratio in which the line joining the point | vedclass

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(D) Let the ratio in which the $xy$-plane divides the line segment joining the points $P(a, b, c)$ and $Q(-a, -c, -b)$ be $k:1$.The coordinates of the

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$c:b$

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(D) Let the ratio in which the $xy$-plane divides the line segment joining the points $P(a, b, c)$ and $Q(-a, -c, -b)$ be $k:1$.The coordinates of the point dividing the segment in ratio $k:1$ are given by the section formula:$\left( \frac{k(-a) + 1(a)}{k+1}, \frac{k(-c) + 1(b)}{k+1}, \frac{k(-b) + 1(c)}{k+1} \right)$Since the point lies on the $xy$-plane,its $z$-coordinate must be $0$:$\frac{-kb + c}{k+1} = 0$This implies $-kb + c = 0$,or $kb = c$.Therefore,$k = \frac{c}{b}$.Thus,the required ratio is $c:b$.

The ratio in which the line joining the points $(a, b, c)$ and $(-a, -c, -b)$ is divided by the $xy$-plane is

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