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The question asks to identify which vectors in the diagram have the same components as vector \( \vec{d} \), meaning they should have the same direction and magnitude. Let's analyze the provided graph and vectors:

1. **Vector \( \vec{d} \)** (orange) points up and to the right (northeast). It has positive components in both the \(x\)- and \(y\)-directions.

Now, let's compare the other vectors:

- **Vector \( \vec{a} \)** (green) points to the left and upwards. It has a negative \(x\)-component and a positive \(y\)-component.
- **Vector \( \vec{b} \)** (pink) points to the right and downwards. It has a positive \(x\)-component and a negative \(y\)-component.
- **Vector \( \vec{c} \)** (blue) points to the right and upwards. It has positive components in both directions (similar to \( \vec{d} \)).

### Conclusion:
Vector \( \vec{c} \) has the same components (positive \(x\)- and \(y\)-directions) as \( \vec{d} \), while the others do not match. So, the correct answer is \( \vec{c} \).

Would you like more details on vector components or any other related questions? 

Here are five additional questions for deeper understanding:

1. What are the components of vector \( \vec{a} \) and how do they differ from vector \( \vec{d} \)?
2. How do you calculate the magnitude of a vector based on its components?
3. How do opposite vectors differ in terms of components and direction?
4. What happens to a vector’s components if it is reflected over the \(x\)- or \(y\)-axis?
5. How can you verify if two vectors are parallel using their components?

**Tip:** Always check both direction and magnitude when comparing vectors for equality!

¿Cuáles de los siguientes vectores tienen la misma componente y que el vector \( \vec{d} \)? Elige todas las respuestas adecuadas.

Learn how to identify which vectors have the same components as vector \( \vec{d} \). This math problem covers key concepts in vector analysis, including the comparison of vector components and direction. Suitable for high school students in Grades 10-12.

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