Projection of a vector onto another - measure of how much two vectors point in the same direction Results in a ***scalar*** $ \vec{a}\cdot\vec{b}=|\vec{a}||\vec{b}|\cos\theta $ $ \vec{a}=3\hat{i}+5\vec{j},\quad\vec{b}=4\hat{i}+8\hat{j} $ $ \vec{a}\cdot\vec{b}=(3\hat{i}+5\vec{j})\cdot(4\hat{i}+8\hat{j})=12+40 = 52 $ - Can be used to find angle between two vectors $ \cos\theta=\frac{\vec{a}\cdot\vec{b}}{|\vec{a}||\vec{b}|}=\frac{52}{\sqrt{3^2+5^2}\sqrt{4^2+8^2}}\approx\frac{52}{52.15} $ $ \theta=\cos^{-1}\bigg(\frac{52}{52.15}\bigg)\approx4.40^\circ $ - Also ***associative*** $ \vec{a}\cdot\vec{b}=\vec{b}\cdot\vec{a} $ - and ***distributive*** $ x\vec{a}\cdot\vec{b}=\vec{a}\cdot x\vec{b}=x(\vec{a}\cdot\vec{b}) $