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.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Trig Review concept. You can view video lessons to learn Trig Review. Or if you need more Trig Review practice, you can also practice Trig Review practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Bompadre's class at MIZZOU.