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Vector A= 293 units @ 61.8 degrees
Vector B=189 units @ 260.4 degrees
Vector  C= 309 units @ 188.7 degrees
 Vector A + Vector B

To calculate the sum of **Vector A** and **Vector B**, we need to break them down into their x and y components using trigonometry.

### Step 1: Components of **Vector A**
- Magnitude: 293 units
- Direction: 61.8°

For the x-component and y-component of **Vector A**:
- \( A_x = A \cdot \cos(\theta_A) = 293 \cdot \cos(61.8°) \)
- \( A_y = A \cdot \sin(\theta_A) = 293 \cdot \sin(61.8°) \)

### Step 2: Components of **Vector B**
- Magnitude: 189 units
- Direction: 260.4° (which is measured counterclockwise from the positive x-axis)

For the x-component and y-component of **Vector B**:
- \( B_x = B \cdot \cos(\theta_B) = 189 \cdot \cos(260.4°) \)
- \( B_y = B \cdot \sin(\theta_B) = 189 \cdot \sin(260.4°) \)

### Step 3: Calculate the sum of the components
The resultant vector **R** is obtained by summing the components of **A** and **B**:
- \( R_x = A_x + B_x \)
- \( R_y = A_y + B_y \)

### Step 4: Resultant magnitude and direction
The magnitude of the resultant vector **R** is:
- \( |R| = \sqrt{R_x^2 + R_y^2} \)

The direction (angle) of the resultant vector is:
- \( \theta_R = \tan^{-1}\left(\frac{R_y}{R_x}\right) \)

Let me compute these values.The resultant vector **A + B** has the following properties:
- **Magnitude**: \( 128.84 \) units
- **Direction**: \( 33.90^\circ \) (measured counterclockwise from the positive x-axis)

Would you like to go over any of the steps in more detail, or ask further questions?

Here are 5 questions that build on this problem:

1. How do we calculate the sum of three vectors including **Vector C**?
2. What is the physical significance of adding vectors in different directions?
3. How does changing the angle of a vector affect its components?
4. How would you find the components of a vector in three-dimensional space?
5. What is the difference between polar and rectangular forms of vectors?

**Tip:** Always ensure angles are measured from the positive x-axis unless otherwise specified.

Vector A= 293 units @ 61.8 degrees, Vector B=189 units @ 260.4 degrees, Vector C= 309 units @ 188.7 degrees. Find Vector A + Vector B.

Learn how to solve vector addition for Vector A (293 units @ 61.8°) and Vector B (189 units @ 260.4°). This step-by-step guide breaks down the components, calculates the resultant vector magnitude (128.84 units), and direction (33.90°), using trigonometry and vector component analysis. Suitable for college-level physics or calculus students.

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