4. Vectors

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4.01 What is a Vector?

4.02 Position Vectors in 3D

4.03 Finding the Length (Magnitude) of a Vector / Distance Between Two Points in 3D

4.04 Vectors in Column / Component Form

4.05 Direction Vectors in 3D

4.06 Finding a Unit Vector in a Particular Direction

4.07 Finding the Vector from A to B

4.08 The Vector Equation of a Line

4.09 Find the Vector Equation of a Line Between Two Points

4.10 The Cartesian Form for an Equation of a Line

4.11 Show that a Point lies on a Line

4.12 Intersecting Line in 3D: 3 Possibilities

4.13a Determining Whether Two Lines are Parallel

4.13b Determining Whether Two Lines Intersect

4.13c Determining Whether Two Lines are Skew

4.14 EXTENSION: Deriving the Scalar (Dot) Product

4.15 Introducing the Scalar Product / Dot Product

4.16 An Example of Using the Scalar Product / Dot Product

4.17 Determining if Two Vectors are Perpendicular

4.18 Finding the Angle between Two Lines

4.19 Finding the Shortest Distance between a Point and a Line

4.20 Introducing the Vector Equation of a Plane

4.21 Find the Vector Equation of the Plane Passing through 3 Points

4.22 EXTENSION: Converting the Vector Equation of a Plane to a Cartesian Equation

4.23 Introducing the Cartesian Equation of a Plane

4.24 An Example of Finding the Cartesian Equation of a Plane

4.25 Finding the Point of Intersection of a Line and a Plane

4.26 Finding the Angle a Line makes as it Intersects a Plane

4.27 Finding the Angle Two Planes make when they Intersect

4.28a Finding the Shortest Distance between a Point and a Plane - Conceptual Method

4.28b Finding the Shortest Distance between a Point and a Plane - Formula Book Method