Perpendicular

Perpendicular

In geometry, the term perpendicular refers to the relationship between two lines which meet at a right angle (90 degrees). The term can also be used to describe a line or plane that is at a right angle to another line or plane. The concept of perpendicularity is fundamental in many areas of mathematics and science, including algebra, calculus, and physics.

Definition

In elementary geometry, the definition of perpendicularity is typically introduced in the context of lines and angles. Two lines are said to be perpendicular if they intersect at a right angle. This definition can be extended to include planes, where a line is perpendicular to a plane if it is perpendicular to every line in the plane that it intersects.

Properties

Perpendicular lines have several important properties. For example, in a Euclidean space, the shortest distance between a point and a line is the line segment that is perpendicular to the line and passes through the point. In addition, the angle between two perpendicular lines is always 90 degrees, regardless of the orientation of the lines.

Applications

Perpendicularity is a fundamental concept in many areas of mathematics and science. In algebra, the concept of perpendicularity is used to define the dot product of two vectors. In calculus, the derivative of a function at a point gives the slope of the line that is perpendicular to the tangent line at that point. In physics, the concept of perpendicularity is used in the study of forces, where the components of a force can be broken down into perpendicular directions.

See also

• Parallel (geometry)
• Orthogonal
• Right angle
• Normal (geometry)

References

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