L ESSON 27 – P ROPERTIES OF P LANES September 5, 2013 Fernando Morales

L EARNING G OALS Recognize a normal to a plane geometrically and algebraically Determine, using properties of a plane different representations of a plane Solve problems relating to lines and planes in three-space

P EER I NSTRUCTION Explain how you can determine the Cartesian equation of the plane containing three non- collinear points A, B, and C? [T, C] Solution: A normal to this plane is determined by calculating the cross product of the direction vectors AB and AC. This results in a vector perpendicular to the plane in which both these vectors lie. Thus, AB x AC = n If we let P(x,y,z) be any point on the plane, then we can find either vectors AP or BP or CP Then we take the dot product, AP · n = 0 and simplify

P EER I NSTRUCTION If and are two perpendicular planes, with normals and, respectively, what can we conclude about their normal vectors ? [T]

P EER I NSTRUCTION If pi1 and pi2 are two parallel planes, with normals n1 and n, respectively, what can we conclude about their normals ? [T]

S NAIL R ACE

R EQUIRED B EFORE N EXT C LASS Make notes of section 8.2 and 8.3 (also copy down the examples into your notes) Section 8.1 # 20, 21, 23, 24, 35, 36 Section 8.2 # 7, 8, 9, 12, 13 Section 8.3 # 4, 5, 8, 10, 11, 16, 17, 18 Review Chapter 6 and 7

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