When a point divides the line joining points with position vectors p and q externally in the ratio m:n, its position vector is:
r=m−nm⋅q−n⋅p
Here, m=2, n=1, p=a−2b, q=2a+b
r=2−12(2a+b)−1(a−2b)
=14a+2b−a+2b
=(4a−a)+(2b+2b)
=3a+4b
The position vector of the required point is 3a+4b.