This takes DC about 9 minutes to deliver.

1. Start with verbal definitions
   1. Define scalar (physical quantity represented by just a number)
      1. Give examples (mass, volume, and density)
   2. Define vector (physical quantity represented by number and direction - size and orientation)
      1. Give examples (velocity (traveling along Grand River to the east at 40 mph), accel, forces)
2. Mathematical representation in 3D
   1. Components of the vector (how much of the vector is in each direction)
   2. Means you need a coordinate system
3. Shift to 2D vector (easier to draw)
   1. Mathematical representation
   2. Graphical representation (draw big)
      1. Vector components can be measured from reference point (origin or elsewhere)
      2. Magnitude can be computed (Pythag)
      3. Orientation can be computed (trig, defined from +x; so be careful)
      4. Can also get components from mag and orientation (trig, defined from +x, so again be careful)
   3. Every vector has a unit vector
      1. Conceptual description (mag of 1; same direction)
      2. Mathematical representation
      3. Vector can be written as product of magnitude and unit vector (This will be useful in the future)
   4. Finally, adding and subtracting vectors
      1. Mathematically, add or subtract scalar components (show addition)
      2. Graphically, tip to tail method (show subtraction)
   5. Some additional notes are online