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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

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$2 \sqrt{21}$

$2 \sqrt{14}$

$\sqrt{53}$

answer is A.

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Detailed Solution

$\begin{array}{l} \frac{x - 2}{6} = \frac{y + 3}{3} = \frac{z - 4}{6} = λ \\ ∴ R = (4, - 2, 6) \end{array} Required distance = \sqrt{16 + 4 + 36} = 2 \sqrt{14} .$

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