Owl: Wind is not just a speed — it has a direction. A push on a box is not just a number of newtons — it points somewhere. Vectors carry both magnitude and direction; scalars carry only size.
In the plane we write ⟨v₁, v₂⟩ or v₁ i + v₂ j. Addition is tip-to-tail geometry; scaling stretches or flips. Unit vectors remember direction with length 1.
We'll draw arrows, move between geometric and component form, and separate two confusions: a vector is not its magnitude alone, and a position vector pinned at the origin is not the same idea as a free sliding arrow — though they share components.