If `ABCD` is quadrilateral whose sides represent vectors in cyclic order, `vecAB` is equivalent is

Options

A. `vec(CA)+vec(CB)`
B. `vec(CD)`
C. `vec(AD)+vec(DC)+vec(CB)`
D. `vec(AD)+vec(BD)`

Explanation

To solve the problem, we need to determine which vector is equivalent to the vector \(\vec{AB}\) in the quadrilateral \(ABCD\) where the sides represent vectors in cyclic order.

### Step-by-Step Solution:

1. **Understanding the Quadrilateral**:
We have a quadrilateral \(ABCD\) with vertices \(A\), \(B\), \(C\), and \(D\). The sides of the quadrilateral represent vectors in a cyclic order: \(\vec{AB}\), \(\vec{BC}\), \(\vec{CD}\), and \(\vec{DA}\).

2. **Identifying the Vector \(\vec{AB}\)**:
We need to find a vector that is equivalent to \(\vec{AB}\). In vector terms, this means we are looking for a vector that has the same magnitude and direction as \(\vec{AB}\).

3. **Considering the Options**:
Let's analyze the options provided to see which vector can be equivalent to \(\vec{AB}\):
- **Option 1: \(\vec{CA}\)**: This vector points from \(C\) to \(A\). It cannot be equivalent to \(\vec{AB}\) since it points in a different direction.
- **Option 2: \(\vec{CD}\)**: This vector points from \(C\) to \(D\). Again, it is not equivalent to \(\vec{AB}\) as it points in a different direction.
- **Option 3: \(\vec{AD}\)**: This vector points from \(A\) to \(D\). It does not match the direction of \(\vec{AB}\).
- **Option 4: \(\vec{AD} + \vec{DB}\)**: This option combines two vectors. The vector \(\vec{AD}\) points from \(A\) to \(D\) and \(\vec{DB}\) points from \(D\) to \(B\). The resultant of these two vectors will indeed point from \(A\) to \(B\) if we consider the cyclic nature of the quadrilateral.

4. **Conclusion**:
The only option that correctly represents the vector \(\vec{AB}\) is the combination of vectors \(\vec{AD} + \vec{DB}\). Therefore, we conclude that:
\[ \vec{AB} = \vec{AD} + \vec{DB} \]

### Final Answer:
\(\vec{AB} = \vec{AD} + \vec{DB}\)