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Session

Three Dimensional Geometry2(The Plane)

Session Objectives

- Normal Form of the Equation of a Plane, Cartesian

Form

- Plane Passing Through a Given Point and

Perpendicular to - a Given Vector, Cartesian Form

- Plane Passing Through a Point and Parallel to Two

Given Lines, - Cartesian Form

- Plane Containing Two Lines, Cartesian Form

- Plane Passing Through Three Points, Cartesian Form

- Passing Through the Intersection of Two Planes

- Angle Between Two Planes, Angle Between a Line

and a Plane

- Intercept Form of a Plane

- Condition of Co-planarity of Two Lines

- Distance of a Point From a Plane

- Class Exercise

Plane

A plane can be defined as a surface such that if

any two points A, B are taken on it, the line

segment AB lies on the surface i.e., every

point on the line segment AB lies on the plane.

Normal Form of the Equation of a Plane

Cartesian Form

Example 1

Example -2

To Reduce the Cartesian Equation to Normal Form

Example -3

Plane Passing Through a Given Point and

Perpendicular to a Given Vector

Cartesian Form

Example 4

Solution Cont.

Plane Passing Through a Point and Parallel to Two

Given Lines

Cartesian Form

Example 5

Solution Cont.

The Cartesian equation of the plane is

Plane Containing Two Lines

Cartesian Form

Example -6

Plane Passing Through Three Points

Cartesian Form

Example 7

Solution Cont.

Passing Through the intersection of Two Planes

Example 8

Solution Cont.

Example 9

If (i) passes through (1, 1, 1), then

Solution Cont.

Angle Between Two Planes

Cont.

Example -10

Example -11

Angle Between a Line and a Plane

Example -12

Intercept Form of a Plane

The equation of a plane intersecting lengths a, b

and c with x-axis, yaxis and z-axis

respectively is

Example 13

Solution Cont.

Substituting the values of a, b and c in (i), we

get

Condition of Co-planarity of Two Lines

Cartesian Form

Example -14

Distance of a Point From a Plane

The line AB intersects the plane at B

Solution Cont.

Cartesian Form

Example 15

Example -16

(No Transcript)

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