The maximum number of rectangualr components in which a vector can be resolved in a plane, is

Options

A. Infinite
B. Four
C. Two
D. One

Answer

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

### Step-by-Step Solution:

1. **Understanding Vector Resolution**: A vector can be resolved into components along specified axes. In a two-dimensional plane, the most common axes are the x-axis and y-axis.

2. **Resolving a Vector**: When a vector \( \vec{A} \) is resolved in a plane, it can be broken down into two components:
- \( A_x \): the component along the x-axis
- \( A_y \): the component along the y-axis

3. **Using Trigonometric Functions**: The components can be calculated using trigonometric functions based on the angle \( \theta \) that the vector makes with the x-axis:
- \( A_x = A \cos(\theta) \)
- \( A_y = A \sin(\theta) \)

4. **Maximum Components**: In a two-dimensional plane, you can only resolve a vector into two perpendicular components (like x and y). Therefore, the maximum number of rectangular components that a vector can be resolved into in a plane is **2**.

5. **Conclusion**: Thus, the answer to the question is that the maximum number of rectangular components in which a vector can be resolved in a plane is **2**.