题目如图1,以正方体的三条棱所在直线为坐标轴,建立空间直角坐标系Oxyz.点P在正方体的对角线AB上,点Q在正方体的棱CD上.(1)当点P为对角线AB的中点,点Q在棱CD上运动时,探究|PQ|的最小值.(2)当点Q为棱CD的中点,点P在对角线AB上运动时,探究|PQ|的最小值.(3)当点P在对角线AB上运动,点Q在棱CD上运动时,探究|PQ|的最小值. The subject is shown in Fig. 1, taking the line where the three prisms of the cube are located as the coordinate axes, and establishing the Orthogonal coordinate system Oxyz. The point P is on the diagonal line AB of the cube and the point Q is on the cube CD. (1) (2) When point Q is the midpoint of the edge CD and point P moves on the diagonal AB, we explore the minimum value of | PQ | | PQ | (3) When point P moves on diagonal AB and point Q moves on edge CD, the minimum value of | PQ | is explored.