The vertex of $\angle PMQ$ refers to the point where the two rays (or vectors) $\overrightarrow{MP}$ and $\overrightarrow{MQ}$ meet. In the diagram you provided, the two vectors meet at point $M$.

Therefore, the vertex of $\angle PMQ$ is point $M$.

Would you like details on how to calculate the angle $\angle PMQ$, or do you have any other questions?

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Here are five related questions:

1. How do you calculate the magnitude of vectors $\overrightarrow{MP}$ and $\overrightarrow{MQ}$?
2. What is the method to determine the angle $\angle PMQ$ using the dot product of vectors?
3. How do you find the direction cosines of vectors $\overrightarrow{MP}$ and $\overrightarrow{MQ}$?
4. Can you determine if vectors $\overrightarrow{MP}$ and $\overrightarrow{MQ}$ are orthogonal?
5. What is the process to find the vector projection of $\overrightarrow{MP}$ on $\overrightarrow{MQ}$?

Tip: When working with vectors, remember that the dot product can be a powerful tool to find angles between them.