The vectors `vec(a), vec(b) and vec(c) ` are related by `vec(c) = vec(a) + vec(b)` . Which diagram below illustrates this relationship ?

Options

A.
B.
C.
D.

Explanation

To solve the problem, we need to analyze the relationship given by the equation \( \vec{c} = \vec{a} + \vec{b} \) and determine which diagram correctly represents this vector relationship.

### Step-by-Step Solution:

1. **Understanding the Vector Addition**:
- The equation \( \vec{c} = \vec{a} + \vec{b} \) indicates that vector \( \vec{c} \) is the resultant of adding vectors \( \vec{a} \) and \( \vec{b} \).
- In vector addition, the tail of the second vector (in this case, \( \vec{b} \)) should start from the head of the first vector (here, \( \vec{a} \)).

2. **Analyzing Diagram A**:
- In Diagram A, if we start from the tail of \( \vec{a} \), it appears that \( \vec{b} \) starts from the head of \( \vec{a} \), but the resultant \( \vec{c} \) does not start from the head of \( \vec{b} \).
- This does not satisfy the relationship \( \vec{c} = \vec{a} + \vec{b} \).
- **Conclusion**: Diagram A is incorrect.

3. **Analyzing Diagram B**:
- In Diagram B, starting from the tail of \( \vec{a} \), we see that \( \vec{b} \) starts from the head of \( \vec{a} \).
- The head of \( \vec{b} \) then represents the head of \( \vec{c} \).
- This correctly illustrates that \( \vec{c} \) is the resultant of \( \vec{a} \) and \( \vec{b} \).
- **Conclusion**: Diagram B is correct.

4. **Analyzing Diagram C**:
- In Diagram C, if we start from the tail of \( \vec{b} \) and then move to \( \vec{c} \), we find that this configuration implies \( \vec{a} \) is not correctly represented as the sum of \( \vec{b} \) and \( \vec{c} \).
- This does not satisfy the relationship \( \vec{c} = \vec{a} + \vec{b} \).
- **Conclusion**: Diagram C is incorrect.

5. **Analyzing Diagram D**:
- In Diagram D, similar to Diagram C, the arrangement does not show \( \vec{c} \) as the resultant of \( \vec{a} \) and \( \vec{b} \).
- This also does not satisfy the relationship \( \vec{c} = \vec{a} + \vec{b} \).
- **Conclusion**: Diagram D is incorrect.

### Final Answer:
The correct diagram that illustrates the relationship \( \vec{c} = \vec{a} + \vec{b} \) is **Diagram B**.