Three-Dimensional Geometry: Planes — Part 1: Equations and forms of a plane: visual lesson, ISC Class 12 Mathematics

Lesson

Three-Dimensional Geometry: Planes, Part 1

Roofs, walls, glass panes and solar panels: flat surfaces in space.

In this lesson you will

Write the vector and Cartesian equations of a plane through a point with a given normal
Read the direction ratios of the normal from the equation of a plane
Find the plane through three non-collinear points
Write a plane in one-point, intercept and normal forms

Part 1 at a glance.

Concept

Four skills for Part 1.
You will learn to	Topic
write the vector and Cartesian equations of a plane through a point with a given normal	equations
read direction ratios of the normal from an equation	normal
find the plane through three points	three points
write a plane in one-point, intercept and normal forms	forms

Diagram

Every line in the plane through $Q$ is perpendicular to the normal $\vec{n}$ (sketch, not to scale).

A plane is fixed by a point $\vec{a}$ on it and a normal $\vec{n}$ : every $\vec{r}$ on it satisfies $(\vec{r} - \vec{a}) \cdot \vec{n} = 0$ .