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Calculus III: Section 12.5
Professor Ensley
Ship Math
September 12, 2011
Professor Ensley (Ship Math) Calculus III: Section 12.5 September 12, 2011 1 / 5
Equation of a plane
Equation of a plane
Professor Ensley (Ship Math) Calculus III: Section 12.5 September 12, 2011 2 / 5
Equation of a plane
Equation of a plane
Professor Ensley (Ship Math) Calculus III: Section 12.5 September 12, 2011 2 / 5
Equation of a plane
Equation of a plane
Example. Show that any two points P and Q on the plane
6x − 3y + 2z = 12, the vector−→PQ is perpendicular to the vector
〈6,−3, 2〉.
Professor Ensley (Ship Math) Calculus III: Section 12.5 September 12, 2011 2 / 5
Parallel planes
Parallel planes
Professor Ensley (Ship Math) Calculus III: Section 12.5 September 12, 2011 3 / 5
Finding a plane determined by three points
Finding a plane determined by three points
Example. Find the equation of the plane determined by the three points(5, 1, 1), (1, 1, 2), and (2, 1, 1).
Professor Ensley (Ship Math) Calculus III: Section 12.5 September 12, 2011 4 / 5
Trace of a plane
Trace of a plane
Professor Ensley (Ship Math) Calculus III: Section 12.5 September 12, 2011 5 / 5