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To solve for the equilibrant force in component form, let's go through the necessary steps:

### Step 1: Resolve each force into components
Forces \( \vec{F}_1 \) and \( \vec{F}_2 \) are given with magnitudes and angles. We can break them into their x (horizontal) and y (vertical) components using the following formulas:

- \( F_{x} = F \cos \theta \)
- \( F_{y} = F \sin \theta \)

#### For \( \vec{F}_1 = 7.05 \, \text{N} \) at \( 45^\circ \):
- \( F_{1x} = 7.05 \cos 45^\circ \)
- \( F_{1y} = 7.05 \sin 45^\circ \)

#### For \( \vec{F}_2 = 5.95 \, \text{N} \) at \( 135^\circ \):
- \( F_{2x} = 5.95 \cos 135^\circ \)
- \( F_{2y} = 5.95 \sin 135^\circ \)

### Step 2: Find the resultant force components
The x and y components of the resultant force \( \vec{R} \) are found by summing the x and y components of \( \vec{F}_1 \) and \( \vec{F}_2 \):

- \( R_x = F_{1x} + F_{2x} \)
- \( R_y = F_{1y} + F_{2y} \)

### Step 3: The equilibrant force
The equilibrant force \( \vec{E} \) is equal in magnitude but opposite in direction to the resultant force \( \vec{R} \). So,

- \( E_x = -R_x \)
- \( E_y = -R_y \)

Now, let me calculate the values.The equilibrant force in component form is:

\[
\vec{E} = (-0.78 \, \text{N}, -9.19 \, \text{N})
\]

This means the equilibrant force has an x-component of approximately \(-0.78 \, \text{N}\) and a y-component of approximately \(-9.19 \, \text{N}\), which acts in the opposite direction of the resultant force.

Would you like to see the detailed process for calculating the resultant, or do you have any further questions?

### Related questions:
1. How do you calculate the magnitude and direction of the equilibrant force?
2. How does changing the angles of the forces affect the equilibrant?
3. What is the relationship between the resultant and the equilibrant forces?
4. How do you resolve a force vector into components for any arbitrary angle?
5. How can you graphically represent the equilibrant and resultant forces?

### Tip:
Always make sure to check the direction of angles in vector problems, as they significantly influence the components.

Let F1 = 7.05 N, 45° and F2 = 5.95 N, 135°. Find the equilibrant force in component form.

Learn how to calculate the equilibrant force for two vectors with magnitudes 7.05 N at 45° and 5.95 N at 135°. This problem involves resolving vectors into components, summing them, and finding the equilibrant. Suitable for high school physics students.

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