Current location - Training Enrollment Network - Mathematics courses - 20 1 1 The solid geometry problem of mathematics and science in Liaoning college entrance examination is done by geometric method (the answer is vector method). See supplementary questions.
20 1 1 The solid geometry problem of mathematics and science in Liaoning college entrance examination is done by geometric method (the answer is vector method). See supplementary questions.
(1) It is proved that ∵ quadrilateral ABCD is square, PD⊥ plane ABCD, PD∑QA, QA = AB = PD.

∴AD=AQ,∠QAD=90

Q is QE⊥PD, and PD is E.

PQC⊥ aircraft dcq;;

∴E is the midpoint of PD == >; QD=QP,QD⊥QP

CD⊥ Yi Zhi surface AQPD== >CD⊥PQ.

∴PQ⊥ surface dry quenching

PQC dry quenching

(2) Analysis: Let the side length of ABCD be 1.

It is easy to know the PCD of BC⊥ plane = = > BC ⊥ PC.

∴bc=cd= 1,pd=2==>; PC =√5 = = & gt; PB=√6

Go through c, CF⊥PB from PB to f, q, QG⊥PB from PB to g, f, HF//QG from QB to h, and connect HC.

∴∠CFH is the plane angle of dihedral angle Q-BP-C.

bc^2=bf*bp==>; 1 = BF *√6 = = & gt; BF=√6/6== >CF=√(BC^2-BF^2)=√30/6

Yi Zhi BQ=DQ=PQ=√2

∴G is the midpoint of PB

QG=√(BQ^2-BG^2)=√2/2

⊿bfh∽⊿bgq==>; Blast furnace/blast furnace = blast furnace /QG = blast furnace /BQ

∴HF=√2/6,BH=√2/3

∵BC⊥BQ

∴ch=√(bc^2+bh^2)=√ 1 1/3

According to the cosine theorem HC 2 = FC 2+FH 2-2 * FC * HF * COS ∠ CFH.

1 1/9 = 5/6+ 1/ 18-2 *√30/6 *√2/6 * cos∠CFH

cos∠CFH=-√ 15/5

∴ The cosine Q-BP-C of dihedral angle is -√ 15/5.