ABCD is a quadrilateral. Forces `vec(AB), vec(CB), vec(CD) and vec(DA)` act along its sides. What is their resultant ?

Options

A. 2`vec(CD)`
B. `2 vec(DA)`
C. `2 vec(BC)`
D. `2 vec(CB)`

Explanation

To find the resultant of the forces acting along the sides of quadrilateral ABCD, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Forces**: The forces acting along the sides of the quadrilateral ABCD are represented as vectors:
- \( \vec{AB} \) (force along side AB)
- \( \vec{BC} \) (force along side BC)
- \( \vec{CD} \) (force along side CD)
- \( \vec{DA} \) (force along side DA)

2. **Draw the Quadrilateral**: Draw quadrilateral ABCD and label the points A, B, C, and D. This will help visualize the forces acting along the sides.

3. **Use Vector Addition**: To find the resultant of the forces, we can use the property of vector addition. We can express the forces in terms of vectors:
- The force \( \vec{BC} \) can be expressed as \( \vec{AB} + \vec{AC} \) (using the triangle law of vector addition).
- The force \( \vec{DA} \) can be expressed as \( \vec{CD} + \vec{CA} \).

4. **Combine the Forces**: We can combine the forces acting along the quadrilateral:
\[ \vec{AB} + \vec{BC} + \vec{CD} + \vec{DA} \]
Rearranging gives us:
\[ \vec{AB} + \vec{BC} + \vec{CD} + \vec{DA} = \vec{AC} + \vec{CA} \]

5. **Resultant Force Calculation**: From the above equation, we can see that:
\[ \vec{AB} + \vec{CD} + \vec{BC} + \vec{DA} = 0 \]
This implies that the resultant of the forces acting along the sides of the quadrilateral is zero.

6. **Conclusion**: Since the forces balance each other out, the resultant force acting on the quadrilateral ABCD is:
\[ \text{Resultant} = \vec{0} \]