16. (Elective 4-4: Coordinate Systems and Parametric Equations)

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In the rectangular coordinate system $xOy$, establish a polar coordinate system with $O$ as the pole and the positive $x$-axis as the polar axis. The polar equation of line $l$ is $\rho(\sin\theta - 3\cos\theta) = 0$. The parametric equation of curve $C$ is $\begin{cases} x = t - \frac{1}{t}, \\ y = t + \frac{1}{t} \end{cases}$ (where $t$ is the parameter). If $l$ and $C$ intersect at points $A$ and $B$, then $|AB| = $ $\_\_\_\_$ .

III. Solution Questions: This section has 6 questions, for a total of 75 points. Show your work, proofs, or calculation steps.