MATH 151 chapter 1 part 4.pptx - MATH 151 Lecture Chapter 1...

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MATH 151 Lecture Please Silence and store all electronic devices . Chapter 1: Introduction to Vectors and Vector Functions 1 Part 4 Chapter 1
section 1.2 PART 2: THE DOT PRODUCT IN COMPONENT FORM Section 1.2: The Dot Product 2
PART 2: THE DOT PRODUCT IN COMPONENT FORM 3 We will need to be able to “solve a triangle” for the next portion of the lecture.
PART 2: THE DOT PRODUCT IN COMPONENT FORM 4 Solving a triangle means to find the measurements of the three angles and the lengths of the three sides
PART 2: THE DOT PRODUCT IN COMPONENT FORM 5 If we are given certain information then we can solve any triangle using either the law of sines or the law of cosines .
PART 2: THE DOT PRODUCT IN COMPONENT FORM 6 We use the law of sines if we are given : 1. Two angles and one side. 2. Two sides and a non-included angle. Caution! Sometimes the law of sines can yield more than one solution or no solution.
PART 2: THE DOT PRODUCT IN COMPONENT FORM 7 We use the law of cosines if we are given : 1. Three sides. 2. Two sides and an included angle. version one: version two: version three:
PART 2: THE DOT PRODUCT IN COMPONENT FORM 8 Consider two vectors a and b with the same tail. Construct the displacement vector a b . Let Θ be the angle between a and b . a b a b Θ Define a , b , a - b in component form: a = b = a - b =
PART 2: THE DOT PRODUCT IN COMPONENT FORM 9 We can see that a , b and a b form a triangle. a b a b Θ We are given two sides of the triangle, a and b ,and the included angle Θ. Therefore, we can solve this triangle using the law of cosines.