Lines and planes: intersecting, perpendicular, parallel

1103059502

Level: 
B
Let \( ABCDV \) be a rectangle based-pyramid, where \( V \) is its apex and \( K \), \( L \), and \( M \) are the midpoints of its edges \( AD \), \( BC \), and \( CV \) respectively. What is the mutual position of planes \( BVK \) and \( DLM \)?
distinct parallel planes
identical planes
intersecting planes

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.

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.

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.