Suppose `veca` is a vector of magnitude 4.5 unit due north. What is the vector (a) `3veca` (b) `-4 veca`?

Answer

To solve the problem, we need to calculate two vectors based on the given vector \( \vec{a} \) which has a magnitude of 4.5 units directed due north.

### Step-by-Step Solution:

1. **Identify the vector \( \vec{a} \)**:
- Given that \( \vec{a} \) has a magnitude of 4.5 units due north, we can represent it as:
\[ \vec{a} = 4.5 \, \text{units} \, \text{(due north)} \]

2. **Calculate \( 3\vec{a} \)**:
- To find \( 3\vec{a} \), we multiply the magnitude of \( \vec{a} \) by 3:
\[ 3\vec{a} = 3 \times 4.5 \, \text{units} \, \text{(due north)} \]
- Performing the multiplication:
\[ 3\vec{a} = 13.5 \, \text{units} \, \text{(due north)} \]

3. **Calculate \( -4\vec{a} \)**:
- To find \( -4\vec{a} \), we multiply the magnitude of \( \vec{a} \) by -4:
\[ -4\vec{a} = -4 \times 4.5 \, \text{units} \, \text{(due north)} \]
- Performing the multiplication:
\[ -4\vec{a} = -18 \, \text{units} \, \text{(due north)} \]
- Since the result is negative, it indicates that the direction is opposite to that of \( \vec{a} \). Therefore, \( -4\vec{a} \) is directed due south:
\[ -4\vec{a} = 18 \, \text{units} \, \text{(due south)} \]

### Final Answers:
- (a) \( 3\vec{a} = 13.5 \, \text{units} \, \text{(due north)} \)
- (b) \( -4\vec{a} = 18 \, \text{units} \, \text{(due south)} \)