Write 'T' for true and 'F' for false in case of each of the following statements
The ray `vec(AB)` is the same as the ray `vec(BA)`

Options

A. True
B. False
C. Cannot be determined
D. None of the above

Answer

To determine whether the ray \( \vec{AB} \) is the same as the ray \( \vec{BA} \), we need to understand the definitions of rays.

1. **Definition of a Ray**: A ray is a part of a line that starts at a point and extends infinitely in one direction. For example, ray \( \vec{AB} \) starts at point A and extends infinitely through point B.

2. **Understanding \( \vec{AB} \)**: The ray \( \vec{AB} \) starts at point A and goes through point B, continuing infinitely in that direction.

3. **Understanding \( \vec{BA} \)**: Conversely, the ray \( \vec{BA} \) starts at point B and goes through point A, extending infinitely in that direction.

4. **Comparison of the Rays**: Since \( \vec{AB} \) starts at A and goes towards B, while \( \vec{BA} \) starts at B and goes towards A, these two rays are not the same. They have different starting points and extend in opposite directions.

5. **Conclusion**: Therefore, the statement "The ray \( \vec{AB} \) is the same as the ray \( \vec{BA} \)" is false.

Final Answer: **F** (False)

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