What is a normal line?

A normal line is a straight line that is perpendicular to a given curve or surface at a specific point. It is used in mathematics and geometry to find the slope of a curve at a particular point or to calculate the equation of a tangent line.

To find the slope of a curve at a specific point, a normal line is drawn through that point which is perpendicular to the tangent line at that point. The slope of the normal line is the negative reciprocal of the slope of the tangent line at that point.

In three-dimensional space, a normal line to a surface at a specific point is perpendicular to the tangent plane at that point. It is used to find the direction of the surface normal, which is important in applications such as computer graphics, engineering, and physics.

Overall, normal lines play a significant role in calculus, geometry, and other branches of mathematics by providing important information about the behavior of curves and surfaces at specific points.