can you draw the graph and solve this problem?

Vector V, is 6.6 units long and points along the negative x axis. Vector V is 8.5 units long and points at +45° to the positive x axis. (a) What are the x and y components of each vector? (b) Determine the sum V, + V2 (magnitude and angle).

The graph above shows the vectors \( \mathbf{V_1} \) and \( \mathbf{V_2} \), along with their resultant vector \( \mathbf{V_R} \).

### Summary of the Problem:
1. **Vector Components:**
   - **\( \mathbf{V_1} \)**: 
     - \( V_{1x} = -6.6 \) units
     - \( V_{1y} = 0 \) units
   - **\( \mathbf{V_2} \)**: 
     - \( V_{2x} = 6.01 \) units
     - \( V_{2y} = 6.01 \) units
2. **Resultant Vector \( \mathbf{V_R} \):**
   - **Magnitude**: 6.04 units
   - **Angle**: Approximately \( -84.7^\circ \) (measured counterclockwise from the positive x-axis).

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Here are five additional questions related to vectors:
1. How do you calculate the dot product of two vectors?
2. What is the cross product of two vectors, and when is it useful?
3. How can vectors be used to describe physical quantities like force or velocity?
4. What is the significance of the angle between two vectors?
5. How can you find the projection of one vector onto another?

**Tip:** Understanding the components of vectors is crucial when dealing with forces, velocities, and other vector quantities in physics.

Can you draw the graph and solve this problem? Vector V1 is 6.6 units long and points along the negative x-axis. Vector V2 is 8.5 units long and points at +45° to the positive x-axis. (a) What are the x and y components of each vector? (b) Determine the sum V1 + V2 (magnitude and angle).

Explore the calculation of vector components and the resultant vector for vectors V1 and V2. This detailed solution includes trigonometric formulas and vector addition, suitable for students in Grades 10-12. Learn how to determine the magnitude and angle of the resultant vector.

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