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

Explanation

To solve the problem, we need to find the vectors \(3\vec{a}\) and \(-4\vec{a}\) given that \(\vec{a}\) is a vector of magnitude 4.5 units directed due north.

### Step-by-step Solution:

1. **Identify the vector \(\vec{a}\)**:
- The vector \(\vec{a}\) has a magnitude of 4.5 units and is directed due north.
- We can represent this vector in component form as:
\[ \vec{a} = 0\hat{i} + 4.5\hat{j} \]
where \(\hat{i}\) is the unit vector in the east direction and \(\hat{j}\) is the unit vector in the north direction.

2. **Calculate \(3\vec{a}\)**:
- To find \(3\vec{a}\), we multiply the vector \(\vec{a}\) by 3:
\[ 3\vec{a} = 3 \times (0\hat{i} + 4.5\hat{j}) = 0\hat{i} + 13.5\hat{j} \]
- Therefore, the vector \(3\vec{a}\) has a magnitude of 13.5 units and is also directed due north.

3. **Calculate \(-4\vec{a}\)**:
- To find \(-4\vec{a}\), we multiply the vector \(\vec{a}\) by -4:
\[ -4\vec{a} = -4 \times (0\hat{i} + 4.5\hat{j}) = 0\hat{i} - 18\hat{j} \]
- Therefore, the vector \(-4\vec{a}\) has a magnitude of 18 units and is directed due south (the negative sign indicates the opposite direction).

### Final Results:
- \(3\vec{a} = 0\hat{i} + 13.5\hat{j}\) (13.5 units due north)
- \(-4\vec{a} = 0\hat{i} - 18\hat{j}\) (18 units due south)