Equations of Lines and Planes in 3D - Wild Linear Algebra A - NJ Wildberger
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Overview
Syllabus
CONTENT SUMMARY: pg 1: @
pg 2: @
pg 3: @
pg 4: @
pg 5: @ special lines in the 2dimensional case; the x and y axes, and lines parallelel to the x and y axes;
pg 6: @ pencils and stacks;
pg 7: @ question: What does the space of all lines look like?; topologically gluing a line to every point on a circle;
pg 8: @ cylinder; Mobius band;
pg 9: @ lines and planes in 3D; planes; cartesian equation of a plane;
pg 10: @ solving a system of equations in 3D; matrix of determinants of minors;
pg 11: @ lines in 3D; two points, point and vector, intersection of 2 planes; parametric equation;
pg 12: @ line in cartesian and parametric form; cartesian form describes 2 planes that meet in a line;
pg 13: @ examples;
pg 14: @ meet of two planes; method found in very few linear algebra texts; a way of introducing parameters; THANKS to EmptySpaceEnterprise
Introduction
Meet of lines
Special lines
Pencils and stacks
What does the spaces of all lines look like?
Two possibilities
The analog of a line in 2D is a plane in 3D
Two planes generally meet in a line
Lines are determined by: two points, point + vector, two planes
Lines also have Cartesian equations
Meet of two planes
Parametric equation for a plane
Parametric to Cartesian plane
Cartesian to parametric plane
Taught by
Insights into Mathematics