Level:
Project ID:
1103212902
Accepted:
1
Clonable:
0
Easy:
0
A cube \( ABCDEFGH \) with an edge length of \( 2 \) units is placed in a coordinate system (see the picture). Let \( S \) be the midpoint of the face \( ABFE \), and let \( K \) and \( L \) be the midpoints of edges \( DH \) and \( CG \) consecutively. Find the standard equation of a plane \( \alpha \) passing through the points \( A \), \( B \) and \( L \), and calculate the distance of the point \( S \) from \( \alpha \).
\( \alpha\colon x+2z-2=0;\ |S\alpha|=\frac{2\sqrt5}{5} \)
\( \alpha\colon x+2z-2=0;\ |S\alpha|=\frac{2\sqrt3}{3} \)
\( \alpha\colon x+2y-2=0;\ |S\alpha|=\frac{2\sqrt5}{5} \)
\( \alpha\colon x+2y-2=0;\ |S\alpha|=\frac{2\sqrt3}{3} \)