The problem is as follows:

Find the modulus of the resultant from the vectors shown in the picture from below:

The alternatives given on my book are:

$\begin{array}{ll}

1.&10\,\textrm{inch}\\

2.&20\,\textrm{inch}\\

3.&10\sqrt{3}\,\textrm{inch}\\

4.&20\sqrt{3}\,\textrm{inch}\\

5.&60\,\textrm{inch}\\

\end{array}$

For this problem the only thing I could come up with is described in my attempt seen in the figure from below:

I thought that it was easy to form a closed polygon and from there I could obtain a sum like this, hence the resultant:

$\vec{r} = \vec{u} + \vec{v} + \vec{w} + \vec{x} + \vec{y} + \vec{z}$

$\vec{x}+\vec{y}+\vec{z}=\vec{w}$

$\vec{w}+\vec{v}=\vec{u}$

$\vec{r}=\vec{u}+\vec{u}+\vec{w}$

For the sake of brevity, I'm omitting units. Since it is known the radius is $\textrm{10 inch}$ then:

$\vec{w}=20$

and from there it can be inferred that:

$\vec{u}=10$

Then:

$\vec{r}=10+10+20=40$

But my answer doesn't appear in the alternatives. Am I doing something wrong? Could it be that Am I misinterpreting the concepts?. I'd like somebody could take a look into this as I'm confused with vectors. Since I believe an auxiliary drawing can be required to aid understanding of the answer I hope that somebody could help me if there is some sort of geometrical manipulation which can be done to solve this problem. I'd like to note that apparently $\textrm{O}$ is the center of the circle.

Find the modulus of the resultant from the vectors shown in the picture from below:

The alternatives given on my book are:

$\begin{array}{ll}

1.&10\,\textrm{inch}\\

2.&20\,\textrm{inch}\\

3.&10\sqrt{3}\,\textrm{inch}\\

4.&20\sqrt{3}\,\textrm{inch}\\

5.&60\,\textrm{inch}\\

\end{array}$

For this problem the only thing I could come up with is described in my attempt seen in the figure from below:

I thought that it was easy to form a closed polygon and from there I could obtain a sum like this, hence the resultant:

$\vec{r} = \vec{u} + \vec{v} + \vec{w} + \vec{x} + \vec{y} + \vec{z}$

$\vec{x}+\vec{y}+\vec{z}=\vec{w}$

$\vec{w}+\vec{v}=\vec{u}$

$\vec{r}=\vec{u}+\vec{u}+\vec{w}$

For the sake of brevity, I'm omitting units. Since it is known the radius is $\textrm{10 inch}$ then:

$\vec{w}=20$

and from there it can be inferred that:

$\vec{u}=10$

Then:

$\vec{r}=10+10+20=40$

But my answer doesn't appear in the alternatives. Am I doing something wrong? Could it be that Am I misinterpreting the concepts?. I'd like somebody could take a look into this as I'm confused with vectors. Since I believe an auxiliary drawing can be required to aid understanding of the answer I hope that somebody could help me if there is some sort of geometrical manipulation which can be done to solve this problem. I'd like to note that apparently $\textrm{O}$ is the center of the circle.

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