Answer:
To represent these three force vectors acting on an object, we'll need to break each force into its horizontal and vertical components using trigonometry.
Let's denote the angles as follows:
- \( \theta_1 = 30^\circ \) for F1
- \( \theta_2 = 35^\circ \) for F2
- We'll denote the angle for F3 as \( \theta_3 \), and it will be determined using the fact that the sum of all forces acting on an object should result in equilibrium.
First, let's find the horizontal and vertical components of each force:
1. For F1:
- Horizontal component: \( F_{1x} = 200 \times \cos(30^\circ) \)
- Vertical component: \( F_{1y} = 200 \times \sin(30^\circ) \)
2. For F2:
- Horizontal component: \( F_{2x} = 150 \times \cos(35^\circ) \)
- Vertical component: \( F_{2y} = 150 \times \sin(35^\circ) \)
3. For F3:
- Horizontal component: \( F_{3x} = 400 \times \cos(\theta_3) \)
- Vertical component: \( F_{3y} = 400 \times \sin(\theta_3) \)
Since the object is in equilibrium, the sum of all horizontal components must equal zero, and the sum of all vertical components must equal zero.
Therefore, you'll need to solve the following system of equations to find \( \theta_3 \):
\[
\begin{cases}
F_{1x} + F_{2x} + F_{3x} = 0 \\
F_{1y} + F_{2y} + F_{3y} = 0
\end{cases}
\]
Once you find \( \theta_3 \), you can find the horizontal and vertical components of F3 and then draw the vector diagram. Let me know if you'd like me to continue with the calculations or if you need further assistance with any step!
