gaokao 2022 Q18

gaokao · China · national-A-science 12 marks 3x3 Matrices Geometric Interpretation of 3×3 Systems
In the pyramid $P - ABCD$, $PD \perp$ base $ABCD$, $CD \parallel AB$, $AD = DC = CB = 1$, $AB = 2$.
(1) Prove that $BD \perp PA$;
(2) Find the sine of the angle between $PD$ and plane $PAB$.
In the pyramid $P - ABCD$, $PD \perp$ base $ABCD$, $CD \parallel AB$, $AD = DC = CB = 1$, $AB = 2$.\\
(1) Prove that $BD \perp PA$;\\
(2) Find the sine of the angle between $PD$ and plane $PAB$.