It is found that `|A+B|=|A|`,This necessarily implies.

Options

A. `vecB = 0 `
B. `vecA, vecB` are antiparallel
C. `vecA, vecB` are perpendicular
D. `vecA * vecB le 0 `

Explanation

To solve the problem where it is given that \( |A + B| = |A| \), we need to analyze the implications of this equation in terms of vector properties.

### Step-by-Step Solution:

1. **Understanding the Equation**:
We start with the equation \( |A + B| = |A| \). This means that the magnitude of the resultant vector \( A + B \) is equal to the magnitude of vector \( A \).

2. **Using the Triangle Inequality**:
According to the triangle inequality for vectors, the magnitude of the sum of two vectors \( |A + B| \) is always less than or equal to the sum of their magnitudes:
\[ |A + B| \leq |A| + |B| \]
Since we know \( |A + B| = |A| \), we can write:
\[ |A| \leq |A| + |B| \]
This inequality is always true, but we need to explore the equality condition.

3. **Equality Condition**:
The equality \( |A + B| = |A| \) holds true if and only if vector \( B \) does not contribute any additional magnitude to the resultant vector. This occurs when \( B \) is a null vector (zero vector) or when \( B \) is in the exact opposite direction of \( A \).

4. **Analyzing the Case of \( B = 0 \)**:
If \( B \) is the zero vector, then:
\[ A + B = A + 0 = A \]
Thus, \( |A + B| = |A| \) holds true.

5. **Analyzing the Case of Anti-Parallel Vectors**:
If \( B \) is anti-parallel to \( A \), we can express \( B \) as:
\[ B = -kA \quad \text{(where \( k \) is a positive scalar)} \]
Then:
\[ |A + B| = |A - kA| = |(1-k)A| \]
For this to equal \( |A| \), we must have \( 1-k = 1 \) or \( k = 0 \), which again leads us back to \( B = 0 \).

6. **Conclusion**:
Therefore, the necessary implication of \( |A + B| = |A| \) is that vector \( B \) must be the zero vector or \( A \) and \( B \) must be anti-parallel with \( B \) having a magnitude that does not exceed that of \( A \).

### Final Answer:
The necessary implication is that \( B \) is either the zero vector or \( A \) and \( B \) are anti-parallel.