1. What is the Slope of Normal Line?

The slope of the normal line to a curve at a given point is the negative reciprocal of the slope of the tangent line at that point. It represents the steepness of the line perpendicular to the tangent at that point on the curve.

2. How Does the Calculator Work?

The calculator uses the normal line slope formula:

Where:

• \( m_{normal} \) — Slope of the normal line (dimensionless)
• \( m_{tangent} \) — Slope of the tangent line (dimensionless)

Explanation: The normal line is always perpendicular to the tangent line, so their slopes are negative reciprocals of each other.

3. Importance of Normal Line Slope

Details: Calculating the normal line slope is essential in geometry, physics, and engineering applications where perpendicular relationships are important, such as in optics (Snell's law) or computer graphics.

4. Using the Calculator

Tips: Enter the slope of the tangent line. The value cannot be zero (as division by zero is undefined). The result will be the slope of the perpendicular normal line.

5. Frequently Asked Questions (FAQ)

Q1: What if the tangent slope is zero?
A: A zero tangent slope means the normal line would be vertical, which has an undefined slope. This is a special case the calculator cannot handle.

Q2: What if the tangent slope is undefined (vertical)?
A: For a vertical tangent line (undefined slope), the normal line would be horizontal with a slope of zero.

Q3: How is this related to derivatives?
A: The tangent slope is the derivative at a point, so this calculator helps find the normal slope once you have the derivative.

Q4: Can this be used for 3D surfaces?
A: In 3D, the normal is a vector perpendicular to the tangent plane, which is more complex than this 2D case.

Q5: What are practical applications?
A: Used in computer graphics for lighting calculations, in physics for reflection angles, and in engineering for stress analysis.