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.