In the figure OE:EA=1:2, AF:FB=3:1 and OG:OB=3:1. The vector OA=a and the vector OB=b.

Find, in terms of a, b or a and b, expressions for:

(a) OE

(b) OF

(c) EF

(d) BG

(e) FB

(f) FG

$\displaystyle OE = \frac{1}{3}a $

$\displaystyle OF = \frac{1}{4}a + \frac{3}{4}b $

$\displaystyle EF= -\frac{1}{12}a + \frac{3}{4}b $

I am stuck on part 'd', my book says vector BG = 2b , and I cannot seem to understand how they got this?

I know OG:OB = 1:3, so does that not mean that $\displaystyle OG = \frac{3}{4}b $ ?

and so to get vector BG , $\displaystyle OG-OB = \frac{3}{4}b - b $

that's my thinking, but the correct answer is BG=2b can someone please show me where I am going wrong.

thank you