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Weifang Ermo Mathematical Solution
(i) When the point on AB satisfies BQ= 13AB, it satisfies the planar AMD of QP∨,

∵MD⊥ plane ABCD, NB⊥ plane ABCD, ∴MD∨nb.

∴ bppm = nbmd = 12,QBQA=232? 23= 12,

∴ qbqa = bppm = 12。 At △MAB, QP∨AM can be obtained.

∵QP? Tablet AMD, AM? Flat AMD.

∴QP∥ plane AMD, that is, find a point Q on the side of AB. When BQ= 13AB, there is qp∑ plane AMD;

(2) Take the straight lines of DA, DC and DM as the X, Y and Z axes respectively, and establish the spatial rectangular coordinate system as shown in the figure.

Get d (0 0,0,0), b (2 2,2,0), c (0 0,2,0), m (0 0,0,2), n (2 2,2, 1).

∴cm=(0,-2,2),cn=(2,0, 1),dc=(0,2,0)

Let the normal vector of CMN plane be m=(x, y, z).

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