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Let $R$ divide line segment $PQ$ in the ratio $k:1$

Hence by section formula, the coordinates of point $R$ are given by,

$(k+1k(8)+2 ,k+1k(0)−3 ,k+1k(10)+4 )=(k+18k+2 ,k+1−3 ,k+110k+4 )$

It is given that the $x$-coordinate of point $R$ is $4$.

$∴k+18k+2 =4$

$⇒8k+2=4k+4$

$⇒4k=2$

$⇒k=21 $

Therefore, the coordinates of point $R$ are $(4,21 +1−3 ,21 +110(21 )+4 )=(4,−2,6)$

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