In the `DeltaABC,AB=a,AC=c and BC=b`, then

Options

A. a+b+c=0
B. a+b-c=0
C. a-b+c=0
D. `-a+b+c=0`

Explanation

To solve the problem, we need to analyze the vectors in triangle ABC with the given sides: AB = a, AC = c, and BC = b. We will express the sides as vectors and use the properties of a triangle to find the correct equation among the provided options.

### Step-by-Step Solution:

1. **Identify the Vectors**:
- Let \( \vec{A} \) represent the vector from point A to point B (i.e., \( \vec{AB} = \vec{A} \)).
- Let \( \vec{B} \) represent the vector from point B to point C (i.e., \( \vec{BC} = \vec{B} \)).
- Let \( \vec{C} \) represent the vector from point C to point A (i.e., \( \vec{CA} = \vec{C} \)).

2. **Set Up the Equation**:
- In a triangle, the sum of the vectors around the triangle must equal zero. Thus, we have:
\[ \vec{AB} + \vec{BC} + \vec{CA} = 0 \]
- Substituting the vectors we defined:
\[ \vec{A} + \vec{B} + \vec{C} = 0 \]

3. **Express CA in Terms of Vectors**:
- Since \( \vec{CA} = -\vec{C} \), we can rewrite the equation:
\[ \vec{A} + \vec{B} - \vec{C} = 0 \]

4. **Rearranging the Equation**:
- Rearranging gives us:
\[ \vec{A} + \vec{B} - \vec{C} = 0 \]
- This implies:
\[ \vec{A} + \vec{B} = \vec{C} \]

5. **Identify the Correct Option**:
- From the equation \( \vec{A} + \vec{B} - \vec{C} = 0 \), we see that the correct option among the given choices is:
\[ \vec{A} + \vec{B} - \vec{C} = 0 \]
- Therefore, the answer is option 2: \( \vec{A} + \vec{B} - \vec{C} = 0 \).