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Find [itex]\vec{a}+\vec{b}[/itex] (Look at the picture)

The book shows the solutions as :

a. 4.1m Along the +x axis.

I however do not know where I went wrong in my calculations.

[itex]\vec{a}+\vec{b}=\begin{bmatrix}

a_x+b_x\\

a_y+b_y

\end{bmatrix}=\begin{bmatrix}

|\vec{a}|\cos(30)+|\vec{b}|\cos(45)\\

|\vec{a}|\sin(30)-|\vec{b}|\sin(45)

\end{bmatrix}=\begin{bmatrix}

\frac{3\sqrt{3}}{2}+\sqrt{2}\\

1.5-\sqrt{2}

\end{bmatrix}=\begin{bmatrix}

4.01\\

.085

\end{bmatrix}[/itex]

NOTE: If I posted this is the wrong location I am sorry. This is not homework, I am doing it on my own time.

EDIT: thank you for moving my post to the correct location.

The book shows the solutions as :

a. 4.1m Along the +x axis.

I however do not know where I went wrong in my calculations.

[itex]\vec{a}+\vec{b}=\begin{bmatrix}

a_x+b_x\\

a_y+b_y

\end{bmatrix}=\begin{bmatrix}

|\vec{a}|\cos(30)+|\vec{b}|\cos(45)\\

|\vec{a}|\sin(30)-|\vec{b}|\sin(45)

\end{bmatrix}=\begin{bmatrix}

\frac{3\sqrt{3}}{2}+\sqrt{2}\\

1.5-\sqrt{2}

\end{bmatrix}=\begin{bmatrix}

4.01\\

.085

\end{bmatrix}[/itex]

NOTE: If I posted this is the wrong location I am sorry. This is not homework, I am doing it on my own time.

EDIT: thank you for moving my post to the correct location.

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