# Beginners Vector problem

1. Feb 1, 2013

### Argyron

I missed 2 weeks of class where we were introduced to vectors and now I have to learn it by myself from the book. I'm stuck on this problem that's part of the assigned homework. If anyone could help me that would be great thanks.
I'm sorry if it's a stupid mistake :/

1. The problem statement, all variables and given/known data
In triangle OAB, $\vec{OA} = a$ and $\vec{OB} = b$
P is a point on AB such that $\vec{AP} = 2\vec{PB}$
and Q is a point such that $\vec{OP} = 3\vec{PQ}$

Express the following in terms of a and b.
a) $\vec{BA}$
b) $\vec{PB}$
c) $\vec{OP}$
d) $\vec{PQ}$
e) $\vec{BQ}$

2. Relevant equations
N/A

3. The attempt at a solution
a) $\vec{BA} = a-b$
b) $\vec{PB} = 1/3(b-a)$

I got stuck on c)
My working out is
$\vec{OP} = \vec{OB} + \vec{BP}$ [Express both vectors in a and b]
$\vec{OP} = b + 1/3(a-b)$
But when I check my answer the book said it was:
$1/3(a+2b)$

Where did I go wrong?

2. Feb 1, 2013

### Pranav-Arora

Solve it further.
$$\vec{OP} = b + 1/3(a-b)=b+a/3-b/3=a/3+2b/3$$

3. Feb 1, 2013

### Argyron

That seems so obvious now that I see it. Thanks for that.

4. Feb 1, 2013

### Pranav-Arora

You are welcome!

Did you solve the rest of the questions?

5. Feb 1, 2013

### Argyron

Yeah, it was easy once I had c.