Vectors summary

Points

• Notation

• Mid point

• Distance

Vectors

• Length

• Dot product

  • Angle between 2 vectors

  • Special cases

• Checking if vectors are parallel/perpendicular

  • For parallel

  • For perpendicular

• Making a normal vector

• Vector Projection

• Checking if moving towards a point

  • Only 1 point moving

  • 2 points moving

• Checking if a moving point will hit line

Syntax

• Alt notation

Info

• Addition

• Subtraction

• Dot product

• Vector projection derivation

Linear equation

• Find using \vec{n} and 1 point

Vector equation

• Notation

• Find vector equation using 2 points

• Linear \to Vector equation

Parametric equation

• Notation

Finding shortest distance

• Point to line

Linear equation

• Proof - Find using \vec{n} and 1 point

Lines

• Notation

• Quick normal vector in 3D

Planes

• Notation

  • Vector equation

    • 3 Points \to Vector equation

    • Vector \to Linear equation

  • Linear equation

Cross product

• Cross product Laws

• Finding area of triangle with cross product

Calculating Distances

• Distances for lines

  • Point to Line

Calculating Angles