MATH 151LecturePlease Silence and storeall electronic devices .Chapter 1: Introduction to Vectors and Vector Functions1Part 4Chapter 1
section 1.2PART 2:THE DOT PRODUCTIN COMPONENTFORMSection 1.2: The Dot Product2
PART 2: THE DOT PRODUCT IN COMPONENT FORM3We will need to beable to “solve atriangle” for the nextportion of the lecture.
PART 2: THE DOT PRODUCT IN COMPONENT FORM4Solving a triangle means tofind the measurements ofthe three angles and thelengths of the three sides
PART 2: THE DOT PRODUCT IN COMPONENT FORM5If we are given certaininformation then we cansolve any triangle using eitherthelaw of sinesorthelaw of cosines.
PART 2: THE DOT PRODUCT IN COMPONENT FORM6We use the law of sines if we are given:1. Two angles and one side.2. Two sides and anon-includedangle.Caution!Sometimesthe law ofsines can yieldmore thanone solutionor no solution.
PART 2: THE DOT PRODUCT IN COMPONENT FORM7We use the law of cosines if we are given:1. Three sides.2. Two sides and anincludedangle.version one:version two:version three:
PART 2: THE DOT PRODUCT IN COMPONENT FORM8Consider two vectorsaandbwith the same tail.Construct the displacement vectora–b.Let Θ be the angle betweenaandb.a–babΘDefinea,b , a - bin component form:a=b=a - b=
PART 2: THE DOT PRODUCT IN COMPONENT FORM9We can see thata,banda–bform a triangle.a–babΘWe are given two sides of the triangle,aandb,and the included angle Θ.Therefore, we can solve this triangle using the law of cosines.