Contents

The Five Lessons

Five lessons, in the order they are meant to be read. The first two build the equations, the third teaches you to draw them, the fourth puts two objects together and asks what happens, and the fifth measures the gap when they miss.

Lesson 01 Equations of Lines in R² and R³ Slope becomes a direction vector, and the vector, parametric and symmetric forms turn out to be one statement written three ways. Ends with the zero denominator that has to be written differently. Lesson 02 Equations of Planes Two directions, or one normal, with the cross product as the bridge between them. Five kinds of given data, all of them a point and two directions in disguise, and the way back from a Cartesian equation to vector form. Lesson 03 Plotting and Sketching in R³ One drawing convention for the whole course, the shadow that makes a plotted point readable, the intercept triangle, and what a missing variable does to a plane. Lesson 04 Intersections and Systems Four cases for two lines, three for a line and a plane, three for two planes, and one table that pairs every algebraic collapse with the picture it describes. Lesson 05 Distances Four distances out of two formulas: point to plane, point to line, and the two parallel cases that reduce to them. Exact answers, and the rescaling trap that makes parallel planes look further apart than they are.