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If ABCD is a square, PD is perpendicular to the plane ABCD, and PD = AB, e is the midpoint of Pb, then the cosine value of the angle formed by the out of plane straight lines PD and AE is? The key is how to express the coordinates of E?
Take D as the origin to establish the space rectangular coordinate system, such that P (0,0,1) a (1,0,0) B (1,1,0) C (0,1,0)
E (1 / 2,1 / 2,1 / 2) [half of the sum of P and B coordinates]
DP=(0,0,1) AE=(-1/2,1/2,1/2)
cos=(1/2)/(1×√3/2)=√3/3
So the cosine of the angle between PD and AE is √ 3 / 3
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