LESSON 27 – PROPERTIES OF PLANESSeptember 5, 2013

Fernando Morales

LEARNING GOALS

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

PEER INSTRUCTION

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

PEER INSTRUCTION

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

PEER INSTRUCTION

If pi1 and pi2 are two parallel planes, with normals n1 and n , respectively, what can we conclude about their normals?

[T]

SNAIL RACE

REQUIRED BEFORE NEXT CLASS

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

QUESTION FER

QUESTION NANDO

QUESTION M

QUESTION S

QUESTION PI