In Part (b) of the problem, we are asked to select all vectors with a y-component of zero.

Let’s analyze the vectors based on their visual directions:

1. Vector 1: This vector is pointing diagonally, indicating both an x and y component are present.
2. Vector 2: This vector points straight up along the y-axis, meaning it has a y-component but no x-component (as noted in Part a).
3. Vector 3: This vector points horizontally to the right along the x-axis, meaning its y-component is zero, while the x-component is nonzero.
4. Vector 4: This vector is also pointing diagonally, meaning both an x and y component are present.

Therefore, the correct answer for Part (b) is Vector 3, as it has a y-component of zero.

Would you like more detailed explanations or have any further questions?

Here are five follow-up questions to expand the understanding:

1. How do you mathematically determine the components of a vector?
2. Can a vector ever have both an x and y component of zero?
3. How do you represent vectors in component form using unit vectors?
4. What is the significance of the magnitude of a vector, and how is it calculated?
5. How can you calculate the direction of a vector relative to the x-axis?

Tip: Always visualize vectors with respect to their components to better understand their direction and magnitude.