Can the coomponent of a vector to greater than vector itself ?

Answer

To determine whether the component of a vector can be greater than the vector itself, we can analyze the situation using basic vector decomposition.

### Step-by-Step Solution:

1. **Understanding Vector Components**:
A vector can be decomposed into components along specified axes. For instance, consider a vector \( \vec{A} \) at an angle \( \theta \) to the horizontal axis. The components of this vector can be represented as:
- \( A_x = A \cos(\theta) \) (horizontal component)
- \( A_y = A \sin(\theta) \) (vertical component)

2. **Magnitude of the Original Vector**:
The magnitude of the vector \( \vec{A} \) is simply \( A \).

3. **Analyzing the Components**:
The maximum values of the sine and cosine functions are both 1. Therefore:
- The maximum value of \( A_x \) occurs when \( \theta = 0^\circ \), giving \( A_x = A \).
- The maximum value of \( A_y \) occurs when \( \theta = 90^\circ \), giving \( A_y = A \).

4. **Comparing Components to the Original Vector**:
- Since \( A_x \) and \( A_y \) can each be at most equal to \( A \), neither component can exceed the magnitude of the original vector \( A \).
- Mathematically, \( A_x \leq A \) and \( A_y \leq A \).

5. **Conclusion**:
Therefore, it is concluded that the components of a vector cannot be greater than the vector itself. The maximum value of each component is equal to the magnitude of the vector when the angle is appropriately chosen (0° for \( A_x \) and 90° for \( A_y \)), but they cannot exceed it.

### Final Answer:
No, the component of a vector cannot be greater than the vector itself.