If `|vec(a)|=3`, what is :
`|5vec(a)|`

Answer

To solve the problem, we need to find the magnitude of the vector \(5\vec{a}\) given that \(|\vec{a}| = 3\).

### Step-by-Step Solution:

1. **Understand the Given Information**:
We know that the magnitude of vector \(\vec{a}\) is given as \(|\vec{a}| = 3\).

2. **Apply the Property of Magnitudes**:
The magnitude of a scalar multiplied by a vector can be expressed as:
\[ |k \vec{a}| = |k| \cdot |\vec{a}| \]
where \(k\) is a scalar. In this case, \(k = 5\).

3. **Calculate the Magnitude**:
Using the property from step 2, we can write:
\[ |5\vec{a}| = |5| \cdot |\vec{a}| \]

4. **Substitute the Known Values**:
We know \(|5| = 5\) (since 5 is a positive scalar) and \(|\vec{a}| = 3\). Therefore, we substitute these values into the equation:
\[ |5\vec{a}| = 5 \cdot 3 \]

5. **Perform the Multiplication**:
Now, we calculate:
\[ |5\vec{a}| = 15 \]

6. **Conclusion**:
Thus, the magnitude of \(5\vec{a}\) is:
\[ |5\vec{a}| = 15 \]

### Final Answer:
\[ |5\vec{a}| = 15 \]