\(A_{\vec{u}} =\)\( \vec{A} \) \( \cdot\) \(\vec{u}\) \( = |\vec{A}| \cos{\theta}\)

\(A_{\vec{u}} = ( A_x \hat{i} + A_y\hat{j}) \cdot (u_x \hat{i} + u_y \hat{j}) =\sqrt{{A_x}^2 +{A_y}^2} \cos{\theta}\)

\(A_{\vec{u}} = \)( \(2.00\) \(\hat{i}\) + \(2.00\) \(\hat{j}\) ) \(\cdot\) ( 1.00 \(\hat{i}\) + 0.00 \(\hat{j}\) ) \(=\) 2.83 \(\cos\)(45\(^\circ\))

\(A_{\vec{u}} = \) 2.00

\(\vec{A}_{\vec{u}}= ( \vec{A}\cdot \vec{u} )\vec{u} =\) 2.00 ( 1.00\(\hat{i}\) + 0.00\(\hat{j}\) ) \(=\) 2.00 \(\hat{i}\) + 0.00 \( \hat{j} \space \)