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What is the ratio in which the line joining the points $(2,4,5)$ and $(3,5,-4)$ is internally divided by the $x y$ -plane?
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The correct answer is:
$5: 4$
Let the line joining the points $(2,4,5)$ and $(3,5,-4)$ is internally divided by the $x y$ - plane in the ratio $k: 1$.
$\therefore \quad$ For xy plane, $z=0$
$\Rightarrow 0=\frac{-\mathrm{k} \times 4+5}{\mathrm{k}+1} \Rightarrow 4 \mathrm{k}=5 \Rightarrow \mathrm{k}=\frac{5}{4}$.
$\mathrm{k}=\frac{5}{4}$ so, ratio is $5: 4$
$\therefore \quad$ For xy plane, $z=0$
$\Rightarrow 0=\frac{-\mathrm{k} \times 4+5}{\mathrm{k}+1} \Rightarrow 4 \mathrm{k}=5 \Rightarrow \mathrm{k}=\frac{5}{4}$.
$\mathrm{k}=\frac{5}{4}$ so, ratio is $5: 4$
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