3-22 할리데이 11판 솔루션 일반물리학

$$\begin{cases} \vec a&=8\i\\ \vec b&=6\j\\ \vec c&=-8\i-6\j\\ \end{cases}$$ $$\ab{a,b}$$ $$\begin{aligned} \vec a\times\vec b&=\(8\i\)\times\(6\j\)\\ &=48\(\i\times\j\)\\ &=48\k\\ \end{aligned}$$ $$\ab{a}$$ $$\abs{\vec a\times\vec b}=48$$ $$\ab{b}$$ $$\text{+z}$$ $$\ab{c,d}$$ $$\begin{aligned} \vec a\times\vec c&=\(8\i\)\times\(-8\i-6\j\)\\ &=8\times(-8)\(\i\times\i\)+8\times(-6)\(\i\times\j\)\\ &=0-48\k\\ &=-48\k \end{aligned}$$ $$\ab{c}$$ $$\abs{\vec a\times\vec c}=48$$ $$\ab{d}$$ $$\text{-z}$$ $$\ab{e,f}$$ $$\begin{aligned} \vec b\times\vec c&=\(6\j\)\times\(-8\i-6\j\)\\ &=6\times(-8)\(\j\times\i\)+6\times(-6)\(\j\times\j\)\\ &=-48(-1)\(\i\times\j\)+0\\ &=48\k\\ \end{aligned}$$ $$\ab{e}$$ $$\abs{\vec b\times\vec c}=48$$ $$\ab{f}$$ $$\text{+z}$$