1. ## Vector arithmetic help

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

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

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

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

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 $OG = \frac{3}{4}b$ ?

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

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

thank you

2. OG = OB + BG
So
OG/OB = 1 + BG/OB
3/1 = 1 + BG/OB
2 = BG/Ob
SO BG = 2OB = 2b.

3. Originally Posted by sa-ri-ga-ma
OG = OB + BG
So
OG/OB = 1 + BG/OB
3/1 = 1 + BG/OB
2 = BG/Ob
SO BG = 2OB = 2b.
thank you, I dont understand how you formed the bold bit,could you just explain why you have divided OG/OB? And where did the one come from?

4. Originally Posted by Tweety
thank you, I dont understand how you formed the bold bit,could you just explain why you have divided OG/OB? And where did the one come from?
The meaning of OG:OB =3:1 is
OG/OB = 3/1

5. Originally Posted by sa-ri-ga-ma
The meaning of OG:OB =3:1 is
OG/OB = 3/1
Okay thanks, get it now. Also if you could explain why it is 1+BG/OB ?

Thank you.

6. OG = OB + BG

Divide OB on both the side.