Given the update:

• Vector $\mathbf{B}$ is now angled at 49.0° relative to the positive x-axis, while its magnitude remains the same at 22.0 units.
• Vector $\mathbf{R}$ has a magnitude of 36.0 units and aligns along the x-axis (since it stretches horizontally).

Steps to solve:

1. Recalculate the components of vector $\mathbf{B}$ with the new angle of 49.0°:

   • $B_x = B \cos(49.0^\circ)$
   • $B_y = B \sin(49.0^\circ)$

2. Determine the components of vector $\mathbf{C}$ using vectors $\mathbf{A}$, $\mathbf{B}$, and $\mathbf{R}$:

   • Since vector $\mathbf{R}$ stretches horizontally, it's parallel to the x-axis.
   • The x-component of $\mathbf{R}$ would then be $R_x = 36.0$ units and $R_y = 0$.

3. Use the vector relationship:

   • Since $\mathbf{C}$ is parallel to $\mathbf{R}$, we need to adjust the relationship to reflect this, possibly adjusting how $\mathbf{C}$ balances the vector sum to align with $\mathbf{R}$.

Let me compute these updated components and the resultant vector $\mathbf{C}$.With the updated angle of vector $\mathbf{B}$ at 49.0°, the magnitude of the resultant vector $\mathbf{C}$ is approximately 31.22 units, and its directional angle $\theta$ relative to the positive x-axis is approximately 32.13°.

This resultant vector $\mathbf{C}$ aligns with vector $\mathbf{R}$, confirming that it is parallel to the x-axis.

Would you like any further details or have any questions?

Here are 5 related questions to explore further:

1. How would the magnitude of $\mathbf{C}$ change if vector $\mathbf{R}$ had a different magnitude?
2. What would happen to the directional angle if vector $\mathbf{B}$ had an angle greater than 90°?
3. How can the vector components be used to analyze the motion of an object in a different scenario?
4. What is the geometric interpretation of having vectors $\mathbf{C}$ and $\mathbf{R}$ parallel?
5. If vector $\mathbf{B}$ were to rotate, how would the resultant vector $\mathbf{C}$ change in magnitude and direction?

Tip: When vectors are parallel, their directional angles are equal or differ by 180°, depending on their direction.