Which of the following relations is correct?

Options

A. `vecA+B=vecC`
B. `vecA+vecB=C`
C. `vecA+vecB=vecC`
D. `A+vecB=vecC`

Answer

To solve the question, we need to analyze the given options and determine which relation is correct based on vector addition properties.

### Step-by-Step Solution:

1. **Understanding Vector Addition**:
- Vectors are quantities that have both magnitude and direction. When we add two vectors, the result is also a vector.
- The general form of vector addition can be expressed as \( \vec{A} + \vec{B} = \vec{C} \).

2. **Analyzing the Options**:
- We need to evaluate each of the given options to see if they correctly represent vector relations.

3. **Option A**: \( \vec{A} + \vec{B} = \vec{C} \)
- This is a standard vector addition equation. If \( \vec{A} \) and \( \vec{B} \) are vectors, then their sum \( \vec{C} \) is also a vector.
- This option is correct.

4. **Option B**: \( \vec{A} + \vec{B} = k \) (where \( k \) is a scalar)
- This option suggests that the sum of two vectors equals a scalar. This is incorrect because the sum of two vectors cannot be a scalar; it must be a vector.

5. **Option C**: \( \vec{A} + \vec{B} = \vec{C} \)
- This is identical to Option A and is also correct for the same reasons.

6. **Option D**: \( \vec{A} = \vec{C} - \vec{B} \)
- This option rearranges the vector equation. Since vector subtraction is valid and \( \vec{C} \) is defined as \( \vec{A} + \vec{B} \), this equation is also valid.
- However, if it implies that \( \vec{A} \) is equal to a scalar, it would be incorrect.

7. **Conclusion**:
- The correct relations based on vector addition are found in Options A and C. However, since the question asks for which of the following relations is correct, the most straightforward answer is that **Option A** or **Option C** is correct.

### Final Answer:
The correct relation is \( \vec{A} + \vec{B} = \vec{C} \).