Table of Contents
- 1 What is the relationship between a line and a plane?
- 2 What is the relationship between a line and a perpendicular line?
- 3 What is the intersection of a plane and a line perpendicular to the plane?
- 4 What is the relationship between two lines in the plane that never intersect each other?
- 5 What is the relationship between the slopes of parallel lines & perpendicular lines?
- 6 What is the intersection of plane and line intersecting it?
What is the relationship between a line and a plane?
These lines have all points in common. Whenever there is no meeting point between a line and a plane, then we can say that the line is parallel to the plane. If a line and a plane have only one point in common, then the line intersects the plane.
What is the relationship between a line and a perpendicular line?
Perpendicular lines are lines that intersect at right angles. If you multiply the slopes of two perpendicular lines in the plane, you get −1 . That is, the slopes of perpendicular lines are opposite reciprocals .
What is the intersection of a plane and a line perpendicular to the plane?
Two planes are perpendicular to each other if and only if one plane contains a line perpendicular to the second plane. If a line is perpendicular to a plane, then every plane containing the line is perpendicular to the given plane. If a plane intersects two parallel planes, then the intersection is two parallel lines.
What is the angle between a line and a plane?
If the straight line is present on the plane or is parallel to it, then the angle formed between the line and plane will be 0 degrees. . This angle that is formed between the line and a plane is actually the angle formed by the straight line with its orthogonal projection on the plane.
Do two planes intersect in a line?
The intersection of two planes is a line. If the planes do not intersect, they are parallel.
What is the relationship between two lines in the plane that never intersect each other?
Two lines, both in the same plane, that never intersect are called parallel lines. Parallel lines remain the same distance apart at all times. The symbol // is used to denote parallel lines.
What is the relationship between the slopes of parallel lines & perpendicular lines?
In other words, the slopes of parallel lines are equal. Note that two lines are parallel if their slopes are equal and they have different y-intercepts. In other words, perpendicular slopes are negative reciprocals of each other.
What is the intersection of plane and line intersecting it?
Answer: If a line and a plane intersect one another, the intersection will be a single point, or a line (if the line lies in the plane). If we want to double-check ourselves, we can plug this coordinate point back into the equation of the plane.
What happens when 2 planes are perpendicular?
Theorem 12: If two planes are perpendicular to the same plane, then the two planes either intersect or are parallel.