This is the tenth lecture in this series on Linear Algebra by N J Wildberger. In this lecture we discuss parametric and Cartesian equations of lines and planes in 3 dimensional affine space. We start by reviewing lines in 2D. A novel feature is the description of all such lines as a Mobius band. For lines and planes in 3D, we avoid the use of inner products and cross products, using determinants instead.CONTENT SUMMARY: pg 1: @00:08review of lines in 2 dimensions; cartesian equation of a line;pg 2: @03:13parametric equation of a line;pg 3: @05:33example: finding? the meet of 2 lines;pg 4: @09:07example: same problem as previous page with lines being described in parametric form;pg 5: @13:07 special lines in the 2dimensional case; the x and y axes, and lines parallelel to the x and y axes;pg 6: @14:41 pencils and stacks;pg 7: @16:52 question: What does the? (space of all lines) look like?; topologically gluing a line to every point on a circle;pg 8: @20:53 cylinder; Mobius band;pg 9: @26:59 lines and planes in 3D; planes; cartesian equation of a plane;pg 10: @30:20 solving a system of equations in 3D; matrix of determinants of minors;pg 11: @35:50 lines in 3D; two points, point and vector, intersection of 2 planes; parametric equation;pg 12: @39:05 line in cartesian and? parametric form; cartesian form describes 2 planes that meet in a line;pg 13: @43:02 examples;pg 14: @47:18 meet of two planes; method found in very few linear algebra texts; a way of introducing parameters; (THANKS to EmptySpaceEnterprise)
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