Two vectors `vecP` and `vecQ` that are perpendicular to each other if :

Explanation

To determine the condition under which two vectors \(\vec{P}\) and \(\vec{Q}\) are perpendicular to each other, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Perpendicular Vectors**:
Two vectors are said to be perpendicular if the angle between them is \(90^\circ\) (or \(\frac{\pi}{2}\) radians).

2. **Dot Product Definition**:
The dot product (or scalar product) of two vectors \(\vec{P}\) and \(\vec{Q}\) is defined as:
\[ \vec{P} \cdot \vec{Q} = |\vec{P}| |\vec{Q}| \cos(\theta) \]
where \(|\vec{P}|\) and \(|\vec{Q}|\) are the magnitudes of the vectors, and \(\theta\) is the angle between them.

3. **Applying the Condition for Perpendicularity**:
Since \(\vec{P}\) and \(\vec{Q}\) are perpendicular, we have:
\[ \theta = 90^\circ \]

4. **Calculating the Cosine of \(90^\circ\)**:
The cosine of \(90^\circ\) is:
\[ \cos(90^\circ) = 0 \]

5. **Substituting into the Dot Product Formula**:
Substituting \(\theta\) into the dot product formula gives:
\[ \vec{P} \cdot \vec{Q} = |\vec{P}| |\vec{Q}| \cdot 0 \]
This simplifies to:
\[ \vec{P} \cdot \vec{Q} = 0 \]

6. **Conclusion**:
Therefore, the condition for the vectors \(\vec{P}\) and \(\vec{Q}\) to be perpendicular is that their dot product must equal zero:
\[ \vec{P} \cdot \vec{Q} = 0 \]

### Final Answer:
Two vectors \(\vec{P}\) and \(\vec{Q}\) are perpendicular to each other if their dot product is equal to zero, i.e., \(\vec{P} \cdot \vec{Q} = 0\).