What are the maximum number of rectangular components of a vector can be split in space and in plane respectively.

Options

A. 3,2
B. 3,3
C. 2,2
D. `infty, infty`

Answer

To solve the question regarding the maximum number of rectangular components a vector can be split into in space and in a plane, we will analyze the dimensions involved.

### Step-by-Step Solution:

1. **Understanding the Dimensions**:
- In physics, we often deal with vectors in different dimensions. The two scenarios we are considering here are:
- **Space**: This refers to three-dimensional space, which includes the x, y, and z axes.
- **Plane**: This refers to two-dimensional space, which includes only the x and y axes.

2. **Components in Space**:
- In three-dimensional space, a vector can be represented with respect to three axes: x-axis, y-axis, and z-axis.
- Any vector in this space can be decomposed into three rectangular components:
- One component along the x-axis
- One component along the y-axis
- One component along the z-axis
- Therefore, the maximum number of rectangular components of a vector in space is **3**.

3. **Components in a Plane**:
- In a two-dimensional plane (like the x-y plane), a vector can be represented with respect to two axes: x-axis and y-axis.
- Any vector in this plane can be decomposed into two rectangular components:
- One component along the x-axis
- One component along the y-axis
- Therefore, the maximum number of rectangular components of a vector in a plane is **2**.

4. **Final Answer**:
- The maximum number of rectangular components of a vector that can be split in space is **3**.
- The maximum number of rectangular components of a vector that can be split in a plane is **2**.

### Summary:
- In space (3D): **3 components**
- In a plane (2D): **2 components**