https://file.aiquickdraw.com/mathbot/file/1724433930940j9yqucxb.jpg

To solve the problem presented in the image, we need to determine the value of the angle \( Q \).

**Analyzing the figure:**
1. There are three vectors drawn, labeled as \( \vec{P} \), \( \vec{Q} \), and \( \vec{R} \).
2. The vectors form angles \( 70^\circ \), \( Q \), and \( 60^\circ \) with the horizontal axis, respectively.

**Assumptions and Approach:**
- The vector \( \vec{P} \) forms an angle of \( 70^\circ \) with the horizontal axis. This angle seems to be measured in the counterclockwise direction.
- The vector \( \vec{Q} \) forms an angle \( Q \) with the horizontal axis.
- The vector \( \vec{R} \) forms an angle of \( 60^\circ \) with the negative horizontal axis, indicating a \( 120^\circ \) angle in the standard counterclockwise direction from the positive horizontal axis.
- Given these angles, we can use the properties of angles in a triangle formed by these vectors or use vector addition rules.

The problem appears to involve vectors and the angles between them. Since the vectors are placed tail-to-tail, the angle sum property can be utilized.

**Steps to find \( Q \):**
1. The total angle around a point is \( 360^\circ \). The angles formed by \( \vec{P} \) and \( \vec{R} \) are given, as \( 70^\circ \) and \( 120^\circ \) respectively.

2. The sum of the angles provided:
   - \( 70^\circ + Q + 120^\circ = 360^\circ \)
   - Simplifying this equation, \( 190^\circ + Q = 360^\circ \).

3. Solve for \( Q \):
   - \( Q = 360^\circ - 190^\circ \)
   - \( Q = 170^\circ \)

Thus, the value of \( Q \) is \( 170^\circ \).

Would you like more details on this problem or have any questions?

Here are some related questions for further exploration:
1. What is the significance of vector angles in physics?
2. How do you calculate the resultant of two vectors given their magnitudes and angles?
3. What is the dot product of two vectors, and how does it relate to the angle between them?
4. How can you use the cross product to find the angle between two vectors?
5. What are some real-world applications where vector angles are important?

**Tip:** When working with vectors, always pay attention to the direction and angle of each vector, as they are crucial for accurate calculations and understanding.

Learn how to find the value of angle Q in a problem involving vector angles. Detailed step-by-step solution provided, analyzing angles formed by vectors and using vector addition rules. Suitable for high school students studying vectors and trigonometry.

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