Answer a is not correct.
consider 3 position vectors OA , OB and OC ,so that B lies on the line AC and the ratio (AB)/(BC) = m/n where m and n are two real numbers.
then the vector OB =[(nOA+mOC)/(m+n)
Apply this formula : in your case m=2 n=1 OC=OX =X (unknown) , OB =b and OA =a : then b = [2x+1a]/3 make x the subject and find x = [3b-a]/2
this is the correct answer that gives the position vector OX in terms of a and b.
work and check the other answers......