To find the product of \( 3 \) and \( \frac{3}{11} \), we multiply the two numbers:
\[ 3 \times \frac{3}{11} = \frac{3 \times 3}{11} = \frac{9}{11} \]
Now, comparing this with the given options:
- A: \( \frac{3}{33} \)
- B: \( \frac{9}{11} \)
- C: \( \frac{9}{33} \)
- D: \( \frac{6}{11} \)
The correct answer is \( \frac{9}{11} \), which corresponds to option B.
Thus, the final answer is \( \text{B: } \frac{9}{11} \).