Rn

Rn

1. Vectors

   • Rn Basics
   • Position Vector
   • Geometric Representation
   • Direction Vector
   • Equality of Vectors
   • Vectors in Standard Position

2. Vector Arithmetics

   • Addition and Its Geometry
   • Subtraction and Its Geometry
   • Scalar Multiplication

3. Working w/ Geometry

   • Parallelograms Bisect
   • Midpoints of Quadrilateral's Sides Form Parallelogram
   • 3 Points Trisecting Line Segment
   • 2 Points Trisecting Line Segment

4. Equation Forms

   • Vector Form
   • Parametric Form
   • Symmetric Form

5. Formulas

   • Length of Vector (2)
   • The Included Angle
     • Formula
     • Implications
   • Projections
   • The Lagrange Identity

6. Problem Solving

   • Equation of Line
     • Equation of Line Given 2 Points
     • Equation of Line Given Point and Parallel Line
   • Intersections
     • Intersection of 2 Lines
     • Lines Through Point A that meet L at Points Distance d from Point B
   • Shapes
     • Prove its a Right Triangle
     • Prove Diagonals of Rhombus are Perpendicular
   • Shortest Distance
     • Point to Line
     • Point to Plane
     • Skew Lines
   • Orthogonal and Planes
     • Vectors Orthogonal to u and v
     • Equation of Plane
   • Area and Volume
     • Area of Parallelogram
     • Area of Triangle
     • Volume of Parallelepiped

7. Vector Terms

   • Parallel Vectors
   • Unit Vector
     • Finding Unit in Same Direction
   • Comparing 2 Vectors Using Their Lengths
   • Orthogonal Vectors

8. Products

   • Dot Product
     • Properties
   • The Cross Product
     • Properties
     • Length
     • Right Hand System of Vectors
   • The Box Product

9. Inequalities

   • Cauchy-Schwarz
   • Triangle

10. Planes