What is the correct expression for \vec{OP}?

[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 :/

Homework Statement

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) $\vec{BQ}$

Homework Equations

N/A

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?

 

[Saitama]

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 :/

Homework Statement

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) $\vec{BQ}$

Homework Equations

N/A

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?

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

 

[Argyron]

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

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

 

[Saitama]

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

You are welcome!

Did you solve the rest of the questions?

 

[Argyron]

You are welcome!

Did you solve the rest of the questions?

Yeah, it was easy once I had c.