# If a point R(4,y,z) lies on the line segment joining the points P(2,–3,4) and Q(8,0,10), then the distance of R from the origin is :

Question:

If a point R(4,y,z) lies on the line segment joining the points P(2,–3,4) and Q(8,0,10), then the distance of R from the origin is :

1. $2 \sqrt{14}$

2. 6

3. $\sqrt{53}$

4. $2 \sqrt{21}$

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 $=\sqrt{16+4+36}=2 \sqrt{14}$