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MA242.003 Day 9 – January 17, 2013 Review: Equations of lines, Section 9.5 Section 9.5 –Planes
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Equations of PLANES in space.
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Different ways to specify a plane:
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Equations of PLANES in space. 1. Give three non-co-linear points. Different ways to specify a plane:
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Equations of PLANES in space. 1. Give three non-co-linear points. Different ways to specify a plane:
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Equations of PLANES in space. 2. Give two non-parallel intersecting lines. Different ways to specify a plane:
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Equations of PLANES in space. 2. Give two non-parallel intersecting lines. Different ways to specify a plane:
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Equations of PLANES in space. Different ways to specify a plane: 3.Specify a point and a normal vector
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Given:
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Equations of PLANES in space.
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Example: Find an equation for the plane containing the point (1,-5,2) with normal vector
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Example: Find an equation for the plane containing the the points P=(1,-5,2), Q=(-3,8,2) and R=(0,-1,4)
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REMARK: How equations of planes occur in problems
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The Geometry of Lines and Planes For us, a LINE in space is a
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The Geometry of Lines and Planes For us, a LINE in space is a Point and a direction vector v =
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The Geometry of Lines and Planes For us, a Plane in space is a
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The Geometry of Lines and Planes For us, a Plane in space is a Point on the plane And a normal vector n =
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Two lines are parallel
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when
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Two lines are parallel when their direction vectors are parallel
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Two lines are perpendicular
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when
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Two lines are perpendicular when their direction vectors are orthogonal
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Two planes are parallel
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when
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Two planes are parallel when Their normal vectors are parallel
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Two planes are perpendicular
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when
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Two planes are perpendicular when Their normal vectors are orthogonal
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A line is parallel to a plane
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when
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A line is parallel to a plane when the direction vector v for the line is orthogonal to the normal vector n for the plane
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A line is perpendicular to a plane
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A line is perpendicular to a plane when
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A line is perpendicular to a plane when the direction vector v for the line is parallel to the normal vector n for the plane
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Example Problems
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