Why does the displacement vector equal r times the unit vector in θ?

[athrun200]

Homework Statement

Before starting the question, we need to find the displacement vector first.
However, I get stuck here.

I would like to ask(in the solution) how to "noted" that $\hat{r}$=r$\hat{e}_{\theta}$?

Can you explain it in detail?

Homework Equations

The Attempt at a Solution

 

[kuruman]

I would like to ask(in the solution) how to "noted" that $\hat{r}$=r$\hat{e}_{\theta}$?

Can you explain it in detail?

There is nothing to explain. You misquoted the solution. It says $\hat{r}$=r$\hat{e}_{r}$. In plain English it says "Vector r is the same as scalar r times a unit vector in the direction of r." I am not sure why there is a "hat" over r instead of an arrow thus making the magnitude r =1, but it is what it is.