Dot Product

Measures the alignment of its operand vectors on a scale of 0 to 1

• $\vec{u}\cdot \vec{v}={\vec{u}}^T\vec{v}$
• $\vec{u}\cdot \vec{v}=\vec{v}\cdot \vec{u}$
• $(\vec{u}+\vec{v})\cdot \vec{w}=\vec{u}\cdot \vec{w}+\vec{v}\cdot \vec{w}$
• $(c\vec{u})\cdot \vec{v}=c(\vec{u}\cdot \vec{w})$
• $||c\vec{v}||=|c|||\vec{v}||$
• $\vec{u}\cdot \vec{u}\ge 0$
• $\vec{u}\cdot \vec{u}=||\vec{u}|{|}^2$
• $\vec{a}\cdot \vec{b}=|a||b|cos\theta$