Official solution
Equation of PQ is
\[{{x - 2} \over {8 - 2}} = {{y + 3} \over {0 - \left( { - 3} \right)}} = {{z - 4} \over {10 - 4}}\]
\[ \Rightarrow \] \[{{x - 2} \over 6} = {{y + 3} \over 3} = {{z - 4} \over 6}\]
Point R (4, y, z) lies on this
\[ \therefore \] \[{{4 - 2} \over 6} = {{y + 3} \over 3} = {{z - 4} \over 6}\]
\[ \Rightarrow \] \[{1 \over 3} = {{y + 3} \over 3} = {{z - 4} \over 6}\]
y = -2 and y = 6
\[ \therefore \] R = (4, -2, 6)
Distance of R(4, -2, 6) from the origin O(0, 0, 0) is
RO = \[\sqrt {{4^2} + {{\left( { - 2} \right)}^2} + {6^2}} \]
= \[\sqrt {56} = 2\sqrt {14} \]