🧊 Introduction to Three Dimensional Geometry

1. Coordinate Axes and Planes in 3D

In 3D geometry, three mutually perpendicular axes (X, Y, and Z) divide space into eight regions called octants. A point is represented by coordinates (x, y, z).

2. Distance Formula

The distance between two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) is given by:

PQ = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

3. Section Formula

The coordinates of the point R which divides the line segment joining points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) internally in the ratio m:n are:

x = (mx₂ + nx₁) / (m + n)
y = (my₂ + ny₁) / (m + n)
z = (mz₂ + nz₁) / (m + n)

Midpoint Formula

If m = n (ratio 1:1), the midpoint coordinates are simply: ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2).