Dot Product

Topics

• Law of Cosines

Properties

$\vec{a}\cdot \vec{b}\equiv ab\cos \theta$

• $\theta$ is the angle between the vectors

$\vec{a}\cdot (\vec{b}+\vec{c})=\vec{a}\cdot \vec{b}+\vec{a}\cdot \vec{c}$

• Dot products are distributive

Linear Algebra

$\mathbf{A}\cdot \mathbf{B}={\mathbf{A}}^{⊺}\mathbf{B}$

Quantum Mechanics

$⟨{\Psi }_m,{\Psi }_n⟩=⟨{\Psi }_m|{\Psi }_n⟩={\int }_{-\infty }^{\infty }{\Psi }_m^{\ast }(x){\Psi }_n(x)\mathrm{d}x$