The maximum number of rectangular components into which a vector in space can be resolved into is

Options

A. two
B. three
C. four
D. any number

Answer

To determine the maximum number of rectangular components into which a vector in space can be resolved, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Vectors in Space**:
A vector in three-dimensional space can be represented in terms of its components along the three coordinate axes: x, y, and z.

2. **Defining Rectangular Components**:
Rectangular components of a vector are the projections of the vector along the axes of a coordinate system. In three-dimensional space, these components are orthogonal (perpendicular) to each other.

3. **Identifying the Axes**:
In a three-dimensional Cartesian coordinate system, there are three axes:
- The x-axis
- The y-axis
- The z-axis

4. **Resolving the Vector**:
Any vector \( \vec{A} \) in space can be resolved into three components:
- \( A_x \) along the x-axis
- \( A_y \) along the y-axis
- \( A_z \) along the z-axis

5. **Conclusion**:
Since there are three mutually perpendicular axes in three-dimensional space, a vector can be resolved into a maximum of three rectangular components.

Thus, the maximum number of rectangular components into which a vector in space can be resolved is **3**.

### Final Answer:
The maximum number of rectangular components into which a vector in space can be resolved is **3**.

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