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