The length of the vector $\left[\begin{array}{c}3 \\ 2 \\ -2 \\ -3\end{array}\right]$ is $\square$.

Step 1 ：Define the vector as \(\left[\begin{array}{c}3 \ 2 \ -2 \ -3\end{array}\right]\).

Step 2 ：Calculate the length of the vector using the formula \(\sqrt{\sum_{i=1}^{n} a_i^2}\), where \(a_i\) are the components of the vector.

Step 3 ：Substitute the values into the formula to get \(\sqrt{3^2 + 2^2 + (-2)^2 + (-3)^2}\).

Step 4 ：Simplify the expression to get \(\sqrt{9 + 4 + 4 + 9}\).

Step 5 ：Further simplify the expression to get \(\sqrt{26}\).

Step 6 ：Calculate the square root of 26 to get approximately 5.099.

Step 7 ：Final Answer: The length of the vector is \(\boxed{5.099}\).