gaokao 2024 Q17

gaokao · China · national-I_github 15 marks Vectors: Lines & Planes Dihedral Angle or Angle Between Planes/Lines
(15 points) As shown in the figure, in the quadrangular pyramid $P - A B C D$ , $P A \perp$ base $A B C D , P A = A C = 2$ , $B C = 1 , A B = \sqrt { 3 }$ .
(1) If $A D \perp P B$ , prove that $A D \|$ plane $P B C$ ;
(2) If $A D \perp D C$ , and the sine of the dihedral angle $A - C P - D$ is $\frac { \sqrt { 42 } } { 7 }$ , find $A D$ . 
(15 points)\\
As shown in the figure, in the quadrangular pyramid $P - A B C D$ , $P A \perp$ base $A B C D , P A = A C = 2$ , $B C = 1 , A B = \sqrt { 3 }$ .\\
(1) If $A D \perp P B$ , prove that $A D \|$ plane $P B C$ ;\\
(2) If $A D \perp D C$ , and the sine of the dihedral angle $A - C P - D$ is $\frac { \sqrt { 42 } } { 7 }$ , find $A D$ .
Paper Questions
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19