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# A line with direction ratio $(2,1,2)$ meets the lines $x=y+a=z\:\;and\:\:x+a=2y=2z$. The coordinates of the points of intersections are ?

$\begin{array}{1 1} (a)\:(2a,3a,a)\: and\: (2a,a,a)\:\:\qquad\:(b)\:(3a,2a,3a)\: and\:(a,a,a)\:\:\qquad\:(c)\:(3a,2a,3a)\:and\:(a,a,2a)\:\:\qquad\:(d)\:(3a,3a,3a)\: and\: (a,a,a) \end{array}$

Out of the four options, option $(b) \: (3a,2a,3a)\:and\:(a,a,a)$ is the correct answer.
Because these two points satisfy the given two lines respectively and
also the $d.r.$ of the line $(2,1,2)$ is proportional to $(3a-a,\:2a-a,\:3a-a)$