Vector components:

$\overline{)\begin{array}{rcl}{\mathit{A}}_{\mathit{x}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{A}}\mathbf{\right|}\mathbf{}\mathbf{cos}\mathbf{}\mathit{\theta}\\ {\mathit{A}}_{\mathit{y}}& {\mathbf{=}}& \mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{A}}\mathbf{\right|}\mathbf{}\mathbf{sin}\mathbf{}\mathit{\theta}\end{array}}$

2D vectors Magnitude:

$\overline{)\mathbf{\left|}\stackrel{\mathbf{\rightharpoonup}}{\mathit{A}}\mathbf{\right|}{\mathbf{=}}\sqrt{{{\mathit{A}}_{\mathit{x}}}^{\mathbf{2}}\mathbf{+}{{\mathit{A}}_{\mathit{y}}}^{\mathbf{2}}}}$

Direction:

$\overline{){\mathbf{tan}}{\mathit{\theta}}{\mathbf{=}}\frac{{\mathit{A}}_{\mathit{y}}}{{\mathit{A}}_{\mathit{x}}}}$

Two forces, F1 and F2, act at a point, as shown in the picture. (Fiqure 1) F_{1} has a magnitude of 8.80 N and is directed at an angle of α-65.0° above the negative x axis in the second quadrant. F_{2} has a magnitude of 5.40 N and is directed at an angle of β = 53.3° below the negative x axis in the third quadrant.

A) What is the *x* component *F*_{x} of the resultant force?

B) What is the *y* component *F*_{y} of the resultant force?

C) What is the magnitude *F* of the resultant force?

D) What is the angle *?* that the resultant force forms with the negative *x* axis? In this problem, assume that positive angles are measured clockwise from the negative *x* axis.

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