0$$^\circ$$
$$A_{\vec{u}} =$$$$\vec{A}$$ $$\cdot$$ $$\vec{u}$$ $$= |\vec{A}| \cos{\theta}$$
$$A_{\vec{u}} = ( A_x \hat{i} + A_y\hat{j}) \cdot (u_x \hat{i} + u_y \hat{j}) =\sqrt{{A_x}^2 +{A_y}^2} \cos{\theta}$$
$$A_{\vec{u}} =$$( $$2.00$$ $$\hat{i}$$ + $$2.00$$ $$\hat{j}$$ ) $$\cdot$$ ( 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 $$\hat{j} \space$$