https://file.aiquickdraw.com/mathbot/file/17298042533916or5vy0t.jpg

The question asks which of the following best represents the sum of vectors \( \vec{A} \) (blue) and \( \vec{B} \) (green), showing three choices.

### Analysis:
1. **Vector \( \vec{A} \)**: Blue, pointing diagonally downward to the right.
2. **Vector \( \vec{B} \)**: Green, pointing straight upward.
3. **Vector Addition \( \vec{A} + \vec{B} \)**: To add vectors graphically, place the tail of vector \( \vec{B} \) at the head of vector \( \vec{A} \). The resultant vector will go from the tail of \( \vec{A} \) to the head of \( \vec{B} \).

The resultant vector should reflect both the direction and magnitude of these two combined.

### Observing the answer choices:
- **Option A**: Points diagonally upward to the left, which doesn't match the expected direction.
- **Option B**: Points straight to the right. This doesn't account for the upward direction contributed by vector \( \vec{B} \).
- **Option C**: Points downward, which is also inconsistent with the expected upward influence of \( \vec{B} \).

None of the provided options seem to perfectly match the correct resultant vector. However, based on this diagram, **Option B** seems the closest, representing the horizontal component of the resultant vector, as the upward component may not be visible in the 2D depiction.

Would you like more details or have any questions?

### Related questions:
1. How do you perform vector addition algebraically?
2. What is the geometric method of vector addition?
3. How can you find the magnitude and direction of a resultant vector?
4. What role does the parallelogram method play in vector addition?
5. What is the difference between scalar and vector quantities?

#### Tip:
For accurate vector addition, always remember to add both the horizontal and vertical components of the vectors.

Which of the following best represents \(\vec{A} + \vec{B}\)?

Learn how to graphically add two vectors, \(\vec{A}\) and \(\vec{B}\), using the tail-to-head method. This example explores which resultant vector best represents the sum in a given set of answer choices. Suitable for students in Grades 10-12.

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