APPC Unit 12:  Intro to Vector Space

Unit 12:  Intro to Vector Space

COVID Era Unit 9 Videos

• Day 39:  Vectors Day 1

  • • Vector Worksheet 1 (You can only do #1 and #2 at this time...)

      • • Vector Worksheet 1 Answers

    • Watch These Someday if you get Bored.  Stuff you missed from the old Honors PC curriculum

      • • • • Video 0.5:  Find the Area of This Triangle

            • Video 1:  The Law of Sines

            • Video 2:  An Example

            • Video 3:  Only True Math Nerds Would Watch This

            • Video 4:  An Identity Interlude

            • Video 5:  The Completion of the Law of Cosines

            • Video 6:  An Example

            • Video 1:  Running a Triangle Solving Business

            • Video 2:  The Possible Cases

            • Video 3:  ASA

            • Video 4:  AAS  

            • Video 5:  AAA

            • Video 6:  SAS

            • Video 7:  Consider Starting the Homework

              • • Try to understand why the LOS is dangerous while the LOC is totally safe

                • Solving Triangles Worksheet 1 (Find and Solve the problems we've talked about)

                • Answers page 1

                • Answers page 2

                • Answers page 3

                • Answers page 4

                • Solving Triangles Worksheet 2

                • Answers page 1

                • Answers page 2

                • Answers page 3

                • Answers page 4

            • Video 1:  The Law of Sines is DANGEROUS

            • Video 2:  SSS

            • Video 3:  Donkeys

            • Video 4:  More on Donkeys

• Day 40:  Algebra 1 in Vector Form, Cartesian Equations and Vector Equations (45)

  • • Vector Notes Sheet

    • Practice the following skills in both Cartesian form AND Vector Form

      • • Video 0.5:  Equations of Lines in Vector Space

        • Video 1:  Let's Race!

        • Video 2:  Standard Cartesian Form 

        • Video 3:  Converting from Cartesian to Vector 

        • Video 4:  Converting from Vector to Cartesian

• Day 41:  OSAS Testing for Juniors Workday, Perpendicular Bisectors 

  • • Review Day 39 and Day 40 lessons and videos

    • There is a Practice Problem or two in today's slides.  OPTIONAL

    • Practice creating and solving an infinite number of Perpendicular Bisector problems like the last problem in the slides

      • • Video 5:  Perpendicular Bisectors

• Day 42:  OSAS Testing Day 2, Finishing Algebra 1 in Vector Form

  • • Thing I STILL haven't had time to teach:

      • • Video 12:  Linear Combinations of Vectors

    • Vector Notes Sheet

    • Finish Vector Worksheet 1 

      • • Vector Worksheet 1 Answers

    • Vector Worksheet 2

      • • Vector Worksheet 2 Answers

    • Vector Worksheet 3 (Skip all problems involving Distance and Projection)

      • • Vector Worksheet 3 Answers

    • Vector Worksheet 4 (Skip all problems involving Distance and Projection)

      • • Vector Worksheet 4 Answers

    • Today's Big Idea

      • • Video 1:  How Many Ways Can You Solve a 2x2 System of Equations?

        • Video 2:  Solving Systems of Equations using Vector Methods BEST METHOD EVER!

        • Video 3:  One More Example

• Day 43:  Finish Day 42, 2D Vector Workday

• • • Video 6:  Vector Projection and Scalar Projection

    • Video 7:  Distance from a Point to a Line (Vector)

    • Video 8:  Distance from a Point to a Line (Cartesian)

    • Finish and then Master ALL of the 2D Worksheets

• Day 44:  3D Vector Basics, Equations of Planes

  • • Transitioning from 2D to 3D

    • Be able to find the norm of a 3D vector

    • Be able to add, subtract, and compute the dot product of any two 3D vectors

    • Be able to find the equation of a line given 2 points

    • Be able to find the equation of a plane given its normal vector and 1 point

    • Find 5 different vectors that are orthogonal to w(2, 6, 3)

    • Find 5 different vectors that are orthogonal to v(8, -5, 2)

• Day 45:  BIG PROBLEM #1,  CLASS PICTURE DAY (45) 

  • • Practice calculating the cross product of two 3D vectors.  Do an infinite number of these

    • Practice BIG PROBLEM #1 an infinite number of times (given 3 points, find the equation of the plane that contains them).  Be sure to VERIFY

• Day 46:  BIG PROBLEM #2, Other topics in 3D

  • • Practice Big Problem #2 an infinite number of times (given 2 planes, find the line of intersection).  Be sure to VERIFY

    • Practice Big Problem #1 an infinite number of times

    • Vector Worksheet 5 (Can't do all of these quite yet, but do the ones you can)

      • • Vector Worksheet 5 Answers

    • Vector Worksheet 6 (Can't do all of these quite yet, but do the ones you can)

      • • Vector Worksheet 6 Answers

• Day 47:  3D Lines, Distance, the rest of the stuff, Doing the Square Problem

  • • Practice Big Problem #1 an infinite number of times

    • Practice Big Problem #2 an infinite number of times

    • Derivation of 3D distance from a point to a line

    • Vector Worksheet 5

      • • Vector Worksheet 5 Answers

    • Vector Worksheet 6

      • • Vector Worksheet 6 Answers

    • Derivation of 3D distance from a point to a line

• Day 48:  Vector Final Requests (45)

  • • Finish all 3D worksheets

    • Practice Big Problem #1 an infinite number of times

    • Practice Big Problem #2 an infinite number of times

• Day 49:  Vector Exam 

• • • YAY!!!  NO HOMEWORK!!!

• Day 50:  Last Day