Unit 7 Jeopardy Review

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7.4a: The Dot Product

Objectives:

• Find the dot product of two vectors and use the Properties of the Dot Product.

• Find the angle between two vectors and determine whether two vectors are orthogonal.

Definitions & Formulas:

• Dot Product

• Orthogonal

• Properties of the Dot Product

• Angle Between Two Vectors

Examples:

Ex1. Finding the Dot Product (+ student example 1)


Ex2. Properties of the Dot Product (+student example 2)


Ex3. Angle Between Two Vectors


student example 3


Ex4. Orthogonal Vectors


student example 4

Problem set 7.4a:

2-14 even

26-30 even

36, 48

7.3a: Vectors

Objectives:  

• Represent vectors as directed line segments.

• Write the component forms of vectors.

• Perform basic vector operations and represent them graphically.

Vector Properties:

Examples:

Example 1. Vector Representation by Directed Line Segments


Example 2. Component Form of a Vector


Example 3. Vector Operations


Student Example


Example 4. Finding a Unit Vector


Example 5. Linear Combination of Unit Vectors


Example 6. Vector Operations


Student Example


Problem Set 7.3a:
# 4-10 even, 17-19, 22, 30, 32, 34

7.2: The Law of Cosines

Objectives:

• Use the Law of Cosines to solve oblique triangles (SSS or SAS).

• Use the Law of Cosines to model and solve real-life problems.

Examples:

Example 1. The Law of Cosines (SSS)


Example 2. The Law of Cosines (SAS)



Student example 1




Example 3. Using Heron's area formula to find the area of a triangle


Student Example




7.2 Problem Set
#2-10 even, 25-28, 31, 39,

7.1: The Law of Sines

Objectives:

• Use the Law of Sines to solve oblique triangles (AAS, ASA, SSA).

• Find the areas of oblique triangles.

• Use the Law of Sines to model and solve real-life problems.

Examples

Example 1. Solving an oblique triangle


Example 2. Solving an oblique triangle 2


Student Example


Ex3. Area of an oblique triangle


Student Example




Example 4. The ambiguous case 1


Example 5. The ambiguous case 2


Example 6. The ambiguous case 3


Student Example


6.1 Problem set
#2-8 even, 20-24, 29, 30, 31, 35, 36