Medium Practice — Set 2

Quick Recap — Cross & Triple Products

• $\vec a\times\vec b$ is perpendicular to both; $|\vec a\times\vec b|=|\vec a||\vec b|\sin\theta$.
• Lagrange: $|\vec a\times\vec b|^2+(\vec a\cdot\vec b)^2=|\vec a|^2|\vec b|^2$.
• Volume of a parallelepiped $=|[\vec a\,\vec b\,\vec c]|$; $[\vec a\,\vec b\,\vec c]=[\vec b\,\vec c\,\vec a]$ (cyclic).
• Moment of a force: $\vec M=\vec r\times\vec F$.