# Checklist for Vectors Many schools have been doing vectors recently. Thought I’ll share a little summary/ checklist I have done for my students.

Basic Concepts

• Operations on Vectors
• Addition & Subtraction
• Scalar multiplication
• Dot Product (Scalar)
1. a • a = |a|2
2. If a ⊥ b, then a • b = 0
3. a • b = b • a
• Cross Product (Vector)
1. a × a = 0
2. a × b = − b × a
• Unit Vectors
• Parallel Vectors ( a = k)
• Collinear Vectors ( Parallel with a common point )
• Ratio Theorem ( Found in MF26)
• Midpoint Theorem
• Directional Cosines
• Angles between two Vectors
• Length of Projection
• Perpendicular Distance

Lines

• Equations
• Vector Form ( : r = a + λb, λ∈ ℜ )
• Parametric Form
• Cartesian Form
• Line & Line
• Parallel ( Directions are parallel to each other. )
• Same ( Same Equations )
• Intersecting ( There is a unique solution for λ and μ. )
• Skewed ( Not parallel AND not Intersecting. )
• Angle between two lines ( Angle between their directions )
• Point & Line
• Foot of Perpendicular
• Perpendicular (Shortest) distance
• Point on Line

Planes

• Equations
• Parametric Form ( π r = a + λb + μc, λ, μ ∈ ℜ )
• Scalar Product Form ( r • n = a • n  = d )
• Cartesian Form
• Point & Plane
• Foot of Perpendicular
• Perpendicular (Shortest) distance
• Distance from O to Plane
• Point on Plane
• Reflection of Point
• Line & Plane
• Relationships
1. Parallel
• Line intersects Plane entirely ( Infinite Solutions )
• Do not intersect ( No Solution )
2. Not Parallel
• Intersects at a point ( One Solution )
• Intersection Point
• Angle between Line & Plane
• Reflection of Line
• Plane & Plane
• Relationships
1. Parallel
• Same ( Infinite Solutions )
• Do not intersect ( No Solution )
2. Not Parallel
• Intersects at a line ( Infinite Solutions )
• Intersection Line ( Use of GC )
• Angle between two Planes ( Angle between their normals )
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