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The question is in Vietnamese and asks about the coordinates of the vector **j** in a 3D coordinate system \( Oxyz \).

To solve this:

1. In a 3D Cartesian coordinate system, the standard basis vectors are defined as:
   - **i** = (1, 0, 0), which is aligned with the x-axis,
   - **j** = (0, 1, 0), which is aligned with the y-axis,
   - **k** = (0, 0, 1), which is aligned with the z-axis.

2. The question asks for the coordinates of the vector **j**. By definition, the vector **j** is (0, 1, 0), meaning it has no component in the x or z directions, but a component of 1 in the y direction.

3. Now, looking at the options:
   - A: (1, 1, 1)
   - B: (1, 0, 1)
   - C: (0, 1, 0) ← This is the correct answer.
   - D: (1, 1, 0)

Since **j** = (0, 1, 0), the correct choice is **C**.

Would you like more details, or do you have any questions about this explanation?

Here are 5 related questions:
1. What are the coordinates of the vector **i** in a 3D space?
2. How are the standard basis vectors used in vector operations like dot product and cross product?
3. What are the properties of vector **k** in the coordinate system?
4. How do you represent a vector as a linear combination of **i**, **j**, and **k**?
5. How can you determine the direction of a vector given its coordinates?

**Tip:** Always remember the standard basis vectors in 3D space: **i** = (1, 0, 0), **j** = (0, 1, 0), and **k** = (0, 0, 1).

Trong không gian với hệ trục tọa độ Oxyz, tọa độ của vector j là gì?

Learn how to find the coordinates of vector j in the 3D coordinate system Oxyz. This problem covers the core concepts of the 3D Cartesian system and the standard basis vectors i, j, and k. Ideal for high school students in Grades 10-12.

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