Vector Intuition Math Example 2

Solution

1. 1
   Step 1: Add component-wise: $\vec{u} + \vec{v} = (2+(-1),\ 3+4) = (1, 7)$.
2. 2
   Step 2: Geometrically, place $\vec{v}$ at the tip of $\vec{u}$.
3. 3
   Step 3: The resultant vector $(1, 7)$ goes from the tail of $\vec{u}$ to the tip of $\vec{v}$.
4. 4
   Step 4: This is the head-to-tail rule (parallelogram law): the diagonal of the parallelogram formed by $\vec{u}$ and $\vec{v}$.