3-1 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} \i&:\text{East}\\ \j&:\text{North}\\ \k&:\text{Up}\\ \end{cases} $$ $$\ab{a}$$ $$ \begin{aligned} \i\cdot\k&=\(1\i+0\j+0\k\)\cdot\(0\i+0\j+1\k\)\\ &=1\cdot0+0\cdot0+0\cdot1\\ &=0 \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \(-\k\)\cdot\(-\j\)&=\bra{0\i+0\j+(-1)\k}\cdot\bra{0\i+(-1)\j+0\k}\\ &=0\cdot0+0\cdot(-1)+(-1)\cdot0\\ &=0 \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} \j\cdot\(-\j\)&=\(0\i+1\j+0\k\)\cdot\bra{0\i+(-1)\j+0\k}\\ &=0\cdot0+1\cdot(-1)+0\cdot0\\ &=-1 \end{aligned} $$ $$\ab{d}$$ $$ \begin{cases} \i\times\j&=\k\\ \j\times\k&=\i\\ \k\times\i&=\j\\ \end{cases} $$ $$ \begin{aligned} \k\times\j&=-\(\j\times\k\)\\ &=-\i \end{aligned} $$ $$\text{West}$$ $$\ab{e}$$ $$ \begin{aligned} \(-\i\)\times\(-\j\)&=\i\times\j\\ &=\k \end{aligned} $$ $$\text{Up}$$ $$\ab{f}$$ $$ \begin{aligned} \(-\k\)\times\(-\j\)&=\k\times\j\\ &=-\(\j\times\k\)\\ &=-\i \end{aligned} $$ $$\text{West}$$