If a point R 4, y, z lies on the line segment joining the points P 2, -3, 4 and Q8, 0, 10, then the distance of R from the origin is

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

A
$2 \sqrt{14}$
B
$6$
C
$\sqrt{53}$
D
$2 \sqrt{21}$

Solution:

$\frac{4}{2} = \frac{- y}{y + 3} = \frac{10 - z}{z - 4} \Rightarrow z = 6 and y = - 2 \Rightarrow R (4, - 2, 6)$

Distance from origin $= \sqrt{16 + 4 + 36} = 2 \sqrt{14} .$

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