- #1

Argyron

- 3

- 0

I'm sorry if it's a stupid mistake :/

## Homework Statement

In triangle OAB, [itex]\vec{OA} = a[/itex] and [itex]\vec{OB} = b[/itex]

P is a point on AB such that [itex]\vec{AP} = 2\vec{PB}[/itex]

and Q is a point such that [itex]\vec{OP} = 3\vec{PQ}[/itex]

Express the following in terms of

**a**and

**b**.

a) [itex]\vec{BA}[/itex]

b) [itex]\vec{PB}[/itex]

c) [itex]\vec{OP}[/itex]

d) [itex]\vec{PQ}[/itex]

e) [itex]\vec{BQ}[/itex]

## Homework Equations

N/A

## The Attempt at a Solution

a) [itex]\vec{BA} = a-b[/itex]

b) [itex]\vec{PB} = 1/3(b-a)[/itex]

I got stuck on c)

My working out is

[itex]\vec{OP} = \vec{OB} + \vec{BP}[/itex] [Express both vectors in

**a**and

**b**]

[itex]\vec{OP} = b + 1/3(a-b)[/itex]

But when I check my answer the book said it was:

[itex]1/3(a+2b)[/itex]

Where did I go wrong?