If a point \( \mathrm{R}(4, \mathrm{y}, \mathrm{z}) \) lies on the line segment joining the poin...

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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 \( R \) from the origin is:
(1) \( 2 \sqrt{14} \)
(2) 6
(3) \( \sqrt{53} \)
(4) \( 2 \sqrt{21} \)
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