Medium Practice — Set 1

Quick Recap — Dot Product Applications

• $\vec a\cdot\vec b=a_1b_1+a_2b_2+a_3b_3$; $\cos\theta=\dfrac{\vec a\cdot\vec b}{|\vec a||\vec b|}$.
• Projection of $\vec a$ on $\vec b$ is $\dfrac{\vec a\cdot\vec b}{|\vec b|}$; work $=\vec F\cdot\vec d$.
• $|\vec a\pm\vec b|^2=|\vec a|^2\pm2\vec a\cdot\vec b+|\vec b|^2$.
• Section formula: the point dividing $\vec a,\vec b$ in ratio $m:n$ is $\dfrac{m\vec b+n\vec a}{m+n}$.