gaokao 2022 Q18

gaokao · China · national-B-science 12 marks Vectors: Lines & Planes Dihedral Angle or Angle Between Planes/Lines
(12 points) As shown in the figure, in tetrahedron $ABCD$, $AD \perp CD, AD = CD, \angle ADB = \angle BDC$, and $E$ is the midpoint of $AC$.
(1) Prove: Plane $BED \perp$ plane $ACD$;
(2) Given $AB = BD = 2, \angle ACB = 60°$, point $F$ is on $BD$. When the area of $\triangle AFC$ is minimum, find the sine of the angle between $CF$ and plane $ABD$. 
(12 points)\\
As shown in the figure, in tetrahedron $ABCD$, $AD \perp CD, AD = CD, \angle ADB = \angle BDC$, and $E$ is the midpoint of $AC$.\\
(1) Prove: Plane $BED \perp$ plane $ACD$;\\
(2) Given $AB = BD = 2, \angle ACB = 60°$, point $F$ is on $BD$. When the area of $\triangle AFC$ is minimum, find the sine of the angle between $CF$ and plane $ABD$.
Paper Questions
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18