1103212904

SubArea: 
Analytical space geometry
Level: 
C
Project ID: 
1103212904
Accepted: 
1
Clonable: 
0
Easy: 
0
A rectangle-based right pyramid \( ABCDV \) with a bottom edge length of \( 6 \) units and the perpendicular height of \( 6 \) units is placed in a coordinate system (see the picture). Let \( S \) be the midpoint of the edge \( AD \). Find the standard equation of the plane \( \alpha \) passing through the points \( B \), \( V \) and \( C \), and calculate the distance of the point \( S \) from \( \alpha \).
\( \alpha\colon 2y+z-12=0;\ d=|S\alpha|=\frac{12\sqrt5}{5} \)
\( \alpha\colon 2x+z-12=0;\ d=|S\alpha|=\frac{12\sqrt5}{5} \)
\( \alpha\colon 2y+z-12=0;\ d=|S\alpha|=\frac{6\sqrt5}{5} \)
\( \alpha\colon 2x+z-12=0;\ d=|S\alpha|=\frac{6\sqrt5}{5} \)