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)
**a**•**a**= |**a**|^{2}- If
**a ⊥ b**, then**a**•**b**= 0 **a**•**b = b • a**

- Cross Product (Vector)
**a**×**a**= 0**a**×**b = − b ×****a**

- Unit Vectors
- Parallel Vectors (
**a**= k**b**) - 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 (
*l*:**r**=**a**+ λ**b**, λ∈ ℜ ) - Parametric Form
- Cartesian Form

- Vector 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**+ λ**b**+ μ**c**, λ, μ ∈ ℜ ) - Scalar Product Form (
**r**•**n**=**a**•**n**= d ) - Cartesian Form

- Parametric Form ( π
- Point & Plane
- Foot of Perpendicular
- Perpendicular (Shortest) distance
- Distance from O to Plane
- Point on Plane
- Reflection of Point

- Line & Plane
- Relationships
- Parallel
- Line intersects Plane entirely ( Infinite Solutions )
- Do not intersect ( No Solution )

- Not Parallel
- Intersects at a point ( One Solution )

- Parallel
- Intersection Point
- Angle between Line & Plane
- Reflection of Line

- Relationships
- Plane & Plane
- Relationships
- Parallel
- Same ( Infinite Solutions )
- Do not intersect ( No Solution )

- Not Parallel
- Intersects at a line ( Infinite Solutions )

- Parallel
- Intersection Line ( Use of GC )
- Angle between two Planes ( Angle between their normals )

- Relationships