A point \( R \) with \( x \)-coordinate 6 lies on the line segment ...

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A point \( R \) with \( x \)-coordinate 6 lies on the line segment joining the points \( P(2,-3,4) \) and \( Q(8,0,10) \). Then distance of \( R \) from origin is
\( \mathrm{P} \)
(1) \( \sqrt{47} \)
(2) \( \sqrt{41} \)
(3) \( \sqrt{53} \)
(4) \( 3 \sqrt{7} \)
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