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.

Discover how to locate the vertex of angle PMQ using vectors in geometry. Understand the concept of vectors meeting at a point, illustrated with a detailed example. This problem involves the dot product formula to calculate angles between vectors. Suitable for high school students.

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