Select the statement about two vector `vecA` and `vecB` .

Options

A. Max value of `|vecA+vecB|` = max value of `|vecA-vecB|`
B. Max value of `|vecA+vecB|` = max value of `|vecA-vecB|`
C. Max value of `|vecA+vecB| lt` max value of `|vecA-vecB|`
D. Insufficient information provided.

Explanation

To solve the problem regarding the two vectors \(\vec{A}\) and \(\vec{B}\), we need to analyze the statements provided and determine the relationship between the magnitudes of the vectors when added and subtracted.

### Step-by-Step Solution:

1. **Understanding Vector Magnitudes**:
- The magnitude of the sum of two vectors \(\vec{A}\) and \(\vec{B}\) can be expressed using the formula:
\[ |\vec{A} + \vec{B}| = \sqrt{|\vec{A}|^2 + |\vec{B}|^2 + 2|\vec{A}||\vec{B}|\cos\theta} \]
where \(\theta\) is the angle between the two vectors.

2. **Magnitude of the Difference of Two Vectors**:
- Similarly, the magnitude of the difference of the two vectors is given by:
\[ |\vec{A} - \vec{B}| = \sqrt{|\vec{A}|^2 + |\vec{B}|^2 - 2|\vec{A}||\vec{B}|\cos\theta} \]

3. **Comparing the Two Magnitudes**:
- We need to compare \( |\vec{A} + \vec{B}| \) and \( |\vec{A} - \vec{B}| \).
- The maximum value of \( |\vec{A} + \vec{B}| \) occurs when \(\theta = 0^\circ\) (vectors are in the same direction), and the maximum value of \( |\vec{A} - \vec{B}| \) occurs when \(\theta = 180^\circ\) (vectors are in opposite directions).

4. **Finding Maximum Values**:
- When \(\theta = 0^\circ\):
\[ |\vec{A} + \vec{B}| = |\vec{A}| + |\vec{B}| \]
- When \(\theta = 180^\circ\):
\[ |\vec{A} - \vec{B}| = ||\vec{A}| - |\vec{B}|| \]

5. **Conclusion**:
- The maximum value of \( |\vec{A} + \vec{B}| \) is always greater than or equal to the maximum value of \( |\vec{A} - \vec{B}| \).
- Therefore, we can conclude that:
\[ \text{Maximum value of } |\vec{A} + \vec{B}| \geq \text{Maximum value of } |\vec{A} - \vec{B}| \]

6. **Selecting the Correct Statement**:
- Based on the analysis, the correct statement is that the maximum value of the magnitude of \(\vec{A} + \vec{B}\) is greater than or equal to the maximum value of the magnitude of \(\vec{A} - \vec{B}\).