Given that `vecP+vecQ = vecP-vecQ`. This can be true when :

Options

A. `vecP = vecQ`
B. `vecQ= vec0 `
C. Neither `vecP` nor `vecQ` is a null vector
D. `vecP` is perpendicular to `vecQ`

Answer

To solve the equation \( \vec{P} + \vec{Q} = \vec{P} - \vec{Q} \) and determine when it holds true, we can follow these steps:

### Step-by-step Solution:

1. **Start with the given equation**:
\[ \vec{P} + \vec{Q} = \vec{P} - \vec{Q} \]

2. **Rearrange the equation**:
To isolate the terms involving \( \vec{Q} \), we can subtract \( \vec{P} \) from both sides:
\[ \vec{Q} = -\vec{Q} \]

3. **Combine like terms**:
Now, add \( \vec{Q} \) to both sides:
\[ \vec{Q} + \vec{Q} = 0 \]
This simplifies to:
\[ 2\vec{Q} = 0 \]

4. **Solve for \( \vec{Q} \)**:
Divide both sides by 2:
\[ \vec{Q} = 0 \]

### Conclusion:
The equation \( \vec{P} + \vec{Q} = \vec{P} - \vec{Q} \) holds true when \( \vec{Q} \) is the zero vector.