Step 1 :We are given two points in three-dimensional space, $P_{1}=(2,-2,3)$ and $P_{2}=(-3,2,-1)$, and we are asked to find the distance between these two points.
Step 2 :The distance between two points in three-dimensional space can be calculated using the Euclidean distance formula, which is given by: \[d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}\]
Step 3 :Substituting the given coordinates into the formula, we get: \[d = \sqrt{(-3-2)^2 + (2-(-2))^2 + (-1-3)^2}\]
Step 4 :Solving the above expression, we get the distance as approximately 7.55.
Step 5 :\(\boxed{7.55}\) is the final answer.