`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 determine the magnitude and direction of the vector \( 4\vec{A} \) given that \( \vec{A} \) has a magnitude of 2.7 units and is directed due east.

### Step-by-Step Solution:

1. **Identify the Magnitude of Vector \( \vec{A} \)**:
- We are given that the magnitude of vector \( \vec{A} \) is 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:
\[ |4\vec{A}| = 4 \times |\vec{A}| = 4 \times 2.7 = 10.8 \text{ units} \]

3. **Determine the Direction of Vector \( 4\vec{A} \)**:
- Since \( \vec{A} \) is directed due east, multiplying by a scalar (in this case, 4) does not change the direction of the vector. Therefore, the direction of \( 4\vec{A} \) remains due east.

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

### Summary:
- **Magnitude**: 10.8 units
- **Direction**: Due east