Vector Algebra

Parallelogram Rule

Means that vector addition is

• Commutative: $\vec{A}+\vec{B}=\vec{B}+\vec{A}$
• Associative: $\left(\vec{A}+\vec{B}\right)+\vec{C}=\vec{A}+\left(\vec{B}+\vec{C}\right)$

Adding Components

$\vec{a}+\vec{b}=⟨a_1+b_1,a_2+b_2,a_3+b_3⟩$

Vector Times Scalar

• $\vec{v}\to s\vec{v}=s⟨v_1,v_2,v_3⟩=⟨s{v}_1,s{v}_2,s{v}_3⟩$
• Distributive law: $(s+d)\vec{v}=s\vec{v}+d\vec{v}$
• $\vec{a}\parallel \vec{b}⟺\vec{a}=s\vec{b}$