The vectors a,b and a+b are

Options

A. collinear
B. coplanar
C. non-coplanar
D. none of these

Explanation

To determine the relationship between the vectors \( \mathbf{a} \), \( \mathbf{b} \), and \( \mathbf{a} + \mathbf{b} \), we need to check if they are collinear, coplanar, non-coplanar, or none of these.

### Step-by-step Solution:

1. **Understanding Coplanarity**:
- Three vectors \( \mathbf{a} \), \( \mathbf{b} \), and \( \mathbf{c} \) are said to be coplanar if they lie in the same plane. This condition is satisfied if one of the vectors can be expressed as a linear combination of the other two.

2. **Identifying the Vectors**:
- In our case, we have the vectors \( \mathbf{a} \), \( \mathbf{b} \), and \( \mathbf{c} = \mathbf{a} + \mathbf{b} \).

3. **Expressing \( \mathbf{c} \) as a Linear Combination**:
- We can express \( \mathbf{c} \) as:
\[ \mathbf{c} = 1 \cdot \mathbf{a} + 1 \cdot \mathbf{b} \]
- Here, \( 1 \) and \( 1 \) are real constants.

4. **Checking the Condition for Coplanarity**:
- Since \( \mathbf{c} \) can be written as a linear combination of \( \mathbf{a} \) and \( \mathbf{b} \), it satisfies the condition for coplanarity.

5. **Conclusion**:
- Therefore, we conclude that the vectors \( \mathbf{a} \), \( \mathbf{b} \), and \( \mathbf{a} + \mathbf{b} \) are coplanar.

### Final Answer:
The vectors \( \mathbf{a} \), \( \mathbf{b} \), and \( \mathbf{a} + \mathbf{b} \) are **coplanar**.