Applications of the dot product to planar geometry II | Wild Linear Algebra A 30 | NJ Wildberger

We continue to discuss aspects of planar geometry related to the dot product. This includes the idea of a linear functional, the point-normal form of a line and normal vectors. We derive the formula for the projection of one vector onto another vector, and the quadrance of a point to a line.

We introduce isometries, and show that reflection in a line perpendicular to a vector is an isometry. The product of two reflections is called a rotation.

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Video Content

00:00 Introduction
03:22 Point-normal form of a line
07:21 Three forms for a line
12:49 Quadrance from point to a line
26:01 Reflections
31:17 Definition. A linear transformation is an isometry for any vectors
39:44 Rotations