If `vecA ` is a vector of magnitude 4 units due east. What is the magnitude and direction of a vector `-4vecA` ?

Options

A. 4 units due east
B. 8 units due east
C. 16 units due east
D. 16 units due west

Explanation

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

### Step-by-Step Solution:

1. **Identify the vector \(\vec{A}\)**:
- The vector \(\vec{A}\) has a magnitude of 4 units and is directed due east.
- In vector notation, we can represent this as:
\[ \vec{A} = 4 \hat{i} \]
where \(\hat{i}\) represents the unit vector in the east direction.

2. **Calculate the vector \(-4\vec{A}\)**:
- To find \(-4\vec{A}\), we multiply the vector \(\vec{A}\) by -4:
\[ -4\vec{A} = -4 \times (4 \hat{i}) = -16 \hat{i} \]

3. **Determine the magnitude of \(-4\vec{A}\)**:
- The magnitude of a vector is given by the absolute value of its coefficient:
\[ |\vec{B}| = |-16| = 16 \text{ units} \]

4. **Determine the direction of \(-4\vec{A}\)**:
- The negative sign indicates that the direction of the vector is opposite to that of \(\vec{A}\). Since \(\vec{A}\) is directed due east, \(-4\vec{A}\) will be directed due west.

5. **Final Result**:
- Therefore, the magnitude of the vector \(-4\vec{A}\) is 16 units and its direction is due west.

### Summary:
- Magnitude: 16 units
- Direction: Due west