Question:
If a point $\mathrm{R}(4, \mathrm{y}, \mathrm{z})$ lies on the line segment joining the points $\mathrm{P}(2,-3,4)$ and $\mathrm{Q}(8,0,10)$, then the distance of $\mathrm{R}$ from the origin is :
Correct Option: 1
Solution:
$\frac{4}{2}=\frac{-y}{y+3}=\frac{10-z}{z-4}$
$\Rightarrow \mathrm{z}=6 \& \mathrm{y}=-2$
$\Rightarrow \mathrm{R}(4,-2,6)$
dist. from origin $=\sqrt{16+4+36}=2 \sqrt{14}$
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