Two vectors are equal if they have the same units, magnitude, and direction.
1. Vectors have magnitude and direction. Scalars have only magnitude.
2. we are allowed to move vectors around as long as magnitude and direction stays the same - they "stay the same vector"
3. We add and substract vectors according to the parallelogram or triangle construction.
4. We construct a COORDINATE SYSTEM (1,2,3-dimensional) using an ORIGIN and UNIT vectors ( X, Y, Z). We can decompose VECTORS in COMPONENTS using these unit vectors.
5. Using a COORDINATE SYSTEM, we can "address" a point in space by giving its COORDINATES. For the 2-dim case, we have encountered CARTESIAN and POLAR coordinates.
6. We can represent the POSITION of a point in space by a POSITION "VECTOR" whose COMPONENTS are the CARTESIAN COORDINATES.
7. DISPLACEMENT denotes a vector which points from one point to another. DISPLACEMENT is INDEPENDENT of the choice of coordinate system, as are vectors in general.