Prove that the points $\left(0,1,7\right)$ , $\left(2,1,9\right)$ , and $\left(6,5,13\right)$ are collinear. Find the ratio in which the first point divides the join of the other two.

This is a long answer type question as classified in NCERT Exemplar

$\begin{array}{l}Giventhateachedgeofthecuboidis2units.\\ \therefore Coordinatesoftheverticesare\\ A\left(2,0,0\right),B\left(2,2,0\right),C\left(0,2,0\right),D\left(0,2,2\right),E\left(0,0,2\right),F\left(2,0,2\right),G\left(2,2,2\right)andO\left(0,0,0\right).\end{array}$