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20 17 Nanchang one-mode mathematical answer
(1) Proof: Let m be the midpoint of BC, even numbers are PM and DM, and according to the meaning of the question, ED∨ED∧.. 12AC.

∵P and m are the midpoint of AB and BC respectively, ∴pm∩... 12ac.

∴ Ed ... PM, ... (3 points)

∴ Quadrilateral PMDE is a parallelogram, ∴EP∥DM.

DM again? Aircraft DBC, sports? Aircraft DBC,

∴PE∥ Plane DBC...(5 points)

(2) Solution: Take the point O as the origin and the straight lines OA, OB and OD as the X, Y and Z axes, respectively, and establish the spatial rectangular coordinate system as shown in the figure. Let |AE|=2, then a (2 2,0,0), b (0 0,2,0) C (-2,0,0),

D (0 0,0,2), E (2 2,0,2), P (1, 1, 0)...(6 points)

∴DA=(2,0? 2)、BC=(? 2,? 2,0)、DB=(0,2,? 2) ...(7 points)

Let the normal vector of the plane PBC be n = (x, y, z),

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