Three forces are pulling on the same object such that the system is in equilibrium. Their magnitudes are F1 = 2.83 N. F= 3.35 N. and F3 = 3.64 N, and they make angles of 0, = 45.0°, 02 = -63.43 and 03 =164.05° with respect to the x-axis, respectively. Required:
a. What is the x-component of the force vector F1?
b. What is the y-component of the force vector F1?

(a) 2.001N

(b) 2.001N

A sketch of the scenario has been attached to this response.

Since only the force vector F₁ is required, the only force shown in the sketch is F₁.

As shown in the sketch;

The x-component of the force vector F₁ =

The y-component of the force vector F₁ =

The magnitude of F₁ as given in the question = 2.83N

The angle that the force makes with respect to the x-axis = 45.0°

Using the trigonometric ratio, we see that;

(a) cos 45.0° =

=>   =  F₁ cos 45.0°

=> =  2.83 cos 45.0°

=> =  2.83 x 0.7071

=> =  2.001N

(b) Also;

sin 45.0° =

=>   =  F₁ sin 45.0°

=>   =  2.83 sin 45.0°

=>   =  2.83 x 0.7071

=>   =  2.001N

Therefore, the x-component and y-component of the force vector F₁ is 2.001N