2000006503
Level:
A
A plane and a point are given. The point is not lying in the plane. How many lines perpendicular to this plane pass through the given point?
\(1\)
\(2\)
\(0\)
infinitely many
Lines and planes: intersecting, perpendicular, parallel
2000006504
Level:
A
A plane and a point are given. The point is not lying in the plane. How many lines parallel to this plane pass through the given point?
infinitely many
\(0\)
\(2\)
\(1\)
1003059501
Level:
B
Let \( \alpha \) and \( \beta \) be planes sharing three different points \( A \), \( B \), and \( C \). The points do not lie on one line. What is the mutual position of these two planes?
identical planes
parallel planes
intersecting planes
1103059401
Level:
B
Let \( ABCDEFGH \) be a cube and \( M \), \( N \), and \( P \) the midpoints of the edges \( BF \), \( EF \), and \( CD \), as seen in the picture. What is the mutual position of the lines \( DM \) and \( NP \)?
skew lines
distinct parallel lines
intersecting lines
1103059402
Level:
B
Let \( ABCDEFGH \) be a cube and \( L \), \( M \) the midpoints of the edges \( AB \) and \( BF \). See the picture. What is the mutual position of lines \( DL \) and \( GM \)?
intersecting lines
distinct parallel lines
skew lines
1103059403
Level:
B
Let \( ABCDEFGH \) be a cube and \( N \) the midpoint of the edge \( EF \). See the picture. What is the mutual position of lines \( BN \) and \( CF \)?
skew lines
distinct parallel lines
intersecting lines
1103059404
Level:
B
Let \( ABCDEFGH \) be a cube and \( X \), \( Z \) the midpoints of the edges \( FB \) and \( FG \). See the picture. What is the mutual position of lines \( XZ \) and \( AH \)?
distinct parallel lines
skew lines
intersecting lines
1103059405
Level:
B
Let \( ABCDEFGH \) be a cube and \( K \), \( L \) the centers of its faces \( ABCD \) and \( BCGF \) consecutively as seen in the picture. What is the mutual position of a line \( KL \) and a plane \( CDH \)?
They share no common point.
The line intersects the plane.
The line lies on the plane.
1103059406
Level:
B
Let \( ABCDEFGH \) be a cube and \( L \), \( N \) the centers of its faces \( BCGF \) and \( ADHE \) consecutively as seen in the picture. What is the mutual position of the line \( LN \) and the plane \( ABG \)?
The line lies on the plane.
The line intersects the plane.
They share no common point.
1103059407
Level:
B
Let \( ABCDV \) be a rectangle based-pyramid, \( V \) is its apex and \( K \), \( L \), and \( M \) are the midpoints of its edges \( AB \), \( BC \), and \( AD \) as seen in the picture. What is the mutual position of the line \( KL \) and the plane \( CV\!M \)?
The line intersects the plane.
The line lies on the plane.
They share no common point.