`vec A ` is a vector of magnitude 2.7 units due east . What is the magnitude and direction of vector 4 `vecA` ?

Options

A. 4 units due east
B. 4 units due west
C. 2.7 units due east
D. 10.8 units due east

Answer

To solve the problem, we need to find the magnitude and direction of the vector \(4 \vec{A}\), given that the vector \(\vec{A}\) has a magnitude of 2.7 units and is directed due east.

### Step-by-Step Solution:

1. **Identify the Magnitude of Vector \( \vec{A} \)**:
- The magnitude of vector \( \vec{A} \) is given as 2.7 units.

2. **Calculate the Magnitude of Vector \( 4 \vec{A} \)**:
- To find the magnitude of \( 4 \vec{A} \), we multiply the magnitude of \( \vec{A} \) by 4:
\[ \text{Magnitude of } 4 \vec{A} = 4 \times \text{Magnitude of } \vec{A} = 4 \times 2.7 = 10.8 \text{ units} \]

3. **Determine the Direction of Vector \( 4 \vec{A} \)**:
- Since \( \vec{A} \) is directed due east and we are multiplying by a positive scalar (4), the direction of \( 4 \vec{A} \) remains the same as that of \( \vec{A} \).
- Therefore, the direction of \( 4 \vec{A} \) is also due east.

4. **Conclusion**:
- The magnitude of vector \( 4 \vec{A} \) is 10.8 units and its direction is due east.

### Final Answer:
- **Magnitude**: 10.8 units
- **Direction**: Due East