Perpendicular lines and planes, obliques, distance
Answers are for parents and teachers.
1
A rectangular parallelepiped has dimensions 4, 4, 7. Find its diagonal.
9
2
Point A is 9 from a plane and the projection of an oblique is 12. Find the oblique.
15
3
Two obliques of lengths 17 and 10 are drawn from one point to a plane, the perpendicular is 8. Find their projections.
15 and 6
4
A cube has edge 5. Find the distance between the skew lines A₁B₁ and BC.
5
5
Why is the vertical edge where two walls meet perpendicular to the floor plane? Explain using the criterion.
The vertical edge is perpendicular to the two floor edges (the bottom edges of the walls), and these two edges intersect; by the criterion the edge is perpendicular to the floor plane.