3-35 할리데이 11판 솔루션 일반물리학

$$\begin{cases} \vec a &= a\i\\ \vec b &= -b\j\\ d&>0 \end{cases}$$ $$\ab{a}$$ $$\begin{aligned} \frac{\vec b}{d}&=\frac{-b\j}{d}\\ &=-\frac{b}{d}\j\\ \end{aligned}$$ $$-\frac{b}{d}\lt0$$ $$\therefore -y$$ $$\ab{b}$$ $$\begin{aligned} \frac{\vec b}{-d}&=\frac{-b\j}{-d}\\ &=\frac{b}{d}\j\\ \end{aligned}$$ $$\frac{b}{d}\gt0$$ $$\therefore +y$$ $$\ab{c}$$ $$\begin{aligned} \vec a \cdot \vec b &=a\cdot0+0\cdot(-b)\\ &=0 \end{aligned}$$ $$\ab{d}$$ $$\begin{aligned} \frac{\vec a \cdot \vec b}{d} &=\frac{a\cdot0+0\cdot(-b)}{d}\\ &=0 \end{aligned}$$ $$\ab{e}$$ $$\begin{aligned} \vec a \times \vec b &=\(a\i\)\times\(-b\j\)\\ &=-ab\(\i\times\j\)\\ &=-ab\k \end{aligned}$$ $$\therefore -z$$ $$\ab{f}$$ $$\begin{aligned} \vec b \times \vec a &=\(-b\j\)\times\(a\i\)\\ &=-ab\(\j\times\i\)\\ &=-ab(-1)\(\i\times\j\)\\ &=ab\k \end{aligned}$$ $$\therefore +z$$ $$\ab{g}$$ $$\begin{aligned} \abs{\vec a \times \vec b} &=\abs{-ab\k}\\ &=ab \end{aligned}$$ $$\ab{h}$$ $$\begin{aligned} \abs{\vec b \times \vec a} &=\abs{ab\k}\\ &=ab \end{aligned}$$ $$\ab{i,j}$$ $$\begin{aligned} \frac{\vec a \times \vec b}{d} &=\frac{-ab\k}{d}\\ &=-\frac{ab}{d}\k\\ \end{aligned}$$ $$\ab{i}$$ $$\begin{aligned} \abs{\frac{\vec a \times \vec b}{d}} &=\abs{-\frac{ab}{d}\k}\\ &=\frac{ab}{d} \end{aligned}$$ $$\ab{j}$$ $$\begin{aligned} \frac{\vec a \times \vec b}{d} &=-\frac{ab}{d}\k\\ \end{aligned}$$ $$\therefore -z$$