What is correct ?

Options

A. `|a-b|=|a|-|b|`
B. `|a-b|le|a|-|b|`
C. `|a-b|ge|a|-|b|`
D. `|a-b|gt|a|-|b|`

Explanation

To solve the question regarding the properties of the modulus of vectors, we need to analyze the given options step by step.

### Step-by-Step Solution:

1. **Understanding the Modulus of Vectors**:
The modulus (or magnitude) of a vector \( \mathbf{a} \) is denoted as \( |\mathbf{a}| \). The question involves the expression \( |\mathbf{a} - \mathbf{b}| \).

2. **Applying the Triangle Inequality**:
The triangle inequality states that for any vectors \( \mathbf{a} \) and \( \mathbf{b} \):
\[ |\mathbf{a} + \mathbf{b}| \leq |\mathbf{a}| + |\mathbf{b}| \]
and
\[ |\mathbf{a} - \mathbf{b}| \geq ||\mathbf{a}| - |\mathbf{b}|| \]
This means that:
\[ |\mathbf{a} - \mathbf{b}| \geq ||\mathbf{a}| - |\mathbf{b}|| \]

3. **Analyzing the Options**:
- **Option A**: \( |\mathbf{a} - \mathbf{b}| = |\mathbf{a}| - |\mathbf{b}| \) - This is not generally true.
- **Option B**: \( |\mathbf{a} - \mathbf{b}| \leq |\mathbf{a}| - |\mathbf{b}| \) - This contradicts the triangle inequality and is false.
- **Option C**: \( |\mathbf{a} - \mathbf{b}| \geq |\mathbf{a}| - |\mathbf{b}| \) - This is true based on the triangle inequality.
- **Option D**: \( |\mathbf{a} - \mathbf{b}| > |\mathbf{a}| - |\mathbf{b}| \) - This may be true in some cases but is not universally applicable.

4. **Conclusion**:
Based on the analysis, the correct answer is **Option C**: \( |\mathbf{a} - \mathbf{b}| \geq |\mathbf{a}| - |\mathbf{b}| \).

### Final Answer:
The correct option is **C**: \( |\mathbf{a} - \mathbf{b}| \geq |\mathbf{a}| - |\mathbf{b}| \).