Three Dimensional Geometry

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Session
Three Dimensional Geometry2(The Plane)
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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

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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.
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Normal Form of the Equation of a Plane
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Cartesian Form
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Example 1
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Example -2
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To Reduce the Cartesian Equation to Normal Form
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Example -3
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Plane Passing Through a Given Point and
Perpendicular to a Given Vector
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Cartesian Form
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Example 4
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Solution Cont.
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Plane Passing Through a Point and Parallel to Two
Given Lines
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Cartesian Form
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Example 5
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Solution Cont.
The Cartesian equation of the plane is
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Plane Containing Two Lines
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Cartesian Form
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Example -6
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Plane Passing Through Three Points
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Cartesian Form
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Example 7
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Solution Cont.
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Passing Through the intersection of Two Planes
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Example 8
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Solution Cont.
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Example 9
If (i) passes through (1, 1, 1), then
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Solution Cont.
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Angle Between Two Planes
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Cont.
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Example -10
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Example -11
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Angle Between a Line and a Plane
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Example -12
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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
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Example 13
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Solution Cont.
Substituting the values of a, b and c in (i), we
get
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Condition of Co-planarity of Two Lines
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Cartesian Form
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Example -14
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Distance of a Point From a Plane
The line AB intersects the plane at B
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Solution Cont.
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Cartesian Form
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Example 15
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Example -16
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