Vector Addition

Adding 2 vectors. $\vec{u}+\vec{v}$

Parallelogram Law

Triangle Law

When $|\vec{u}|+|\vec{v}|=|\vec{u}+\vec{v}|$

Only happens in 2 cases:

1. Either $\vec{v}$ or $\vec{u}$ are 0
2. If $\vec{u}$ = $k\vec{v}$. $|\vec{u}+\vec{v}|\le |\vec{u}|+|\vec{v}|$. $kϵN$

Vector Addition Properties

Commutative

$\vec{u}+\vec{v}=\vec{v}+\vec{u}$

Associative

Adding 3+ vectors can be done in any order $\vec{u}+\vec{v}+\vec{r}+\cdots =\vec{r}+\vec{v}+\vec{u}+\cdots =\vec{v}+\vec{u}+\vec{r}+\dots$

Identity Property

Adding a vector of magnitude 0 to another vector will not change the vector at all. It retains its identity. $\vec{v}=0$ $\vec{u}+\vec{v}=\vec{u}$