Three-Dimensional Geometry: Planes — Part 2: Distances, meeting points and angles: visual lesson, ISC Class 12 Mathematics

Lesson

Three-Dimensional Geometry: Planes, Part 2

How far is a point from a plane, where does a line pierce it, and at what angle?

In this lesson you will

Part 2 at a glance.

Concept

Four skills for Part 2.
You will learn to	Topic
find the distance of a point from a plane, and the foot and image	distance
find the distance between parallel planes	parallel planes
find where a line meets a plane, or show it is parallel	line and plane
find the angle between two planes and between a line and a plane	angles

Diagram

$PF$ runs along the normal; $PF = \dfrac{|\vec{n} \cdot \vec{p} - d|}{|\vec{n}|}$ (sketch, not to scale).

The shortest path from $P$ to the plane runs along the normal and meets it at the foot $F$ .