Planes in Three-Dimensional Space

This section covers the comprehensive theory of planes and their equations.

Definition: A general plane equation is E: x = P + λv₁ + μv₂, where λ,μ ∈ ℝ

Highlight: Four distinct methods are presented for establishing plane equations:

1. Through three points
2. Through a line and a point
3. Through two parallel lines
4. Through two intersecting lines

Example: Detailed example showing plane equation construction through points A(1|2|4), B(3|3|4), and C(6|6|8).

Advanced Plane Relationships

This section explores more complex relationships between lines and planes.

Highlight: Special attention is given to:

• Planes through lines and points
• Planes through parallel lines
• Planes through intersecting lines

Example: Multiple practical examples demonstrate different scenarios of lagebeziehung gerade ebene aufgaben.