The Midpoint and Distance Formulas in 3D - Concept

Concept Concept (1)

There are two formulas that are important to remember when considering vectors or positions in the 3D coordinate System. The midpoint formula and the distance formula in 3D. The midpoint and distance formula in 3D can be derived using a method of addition of the geometric representation of vectors. In order to understand the derivation of the distance formula in 3D we must understand 3D vector operations.

Sample Sample Problems (4)

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The Midpoint and Distance Formulas in 3D - Problem 1
Problem 1
How to find the length and midpoint of a segment in three dimensions.
The Midpoint and Distance Formulas in 3D - Problem 2
Problem 2
How to find the equation of a sphere with center (a,b,c) and radius r.
The Midpoint and Distance Formulas in 3D - Problem 3
Problem 3
How to find the equation of the set of points equidistant from two given points.
The Midpoint and Distance Formulas in 3D - Problem 4
Problem 4
How to find the center and radius of a sphere when its equation is not in center-radius form by completing the square.