3-11 할리데이 10판 솔루션 일반물리학

$$\begin{cases} \vec a =\(4.0\ut{m} \)\hat i + \(3.0\ut{m} \)\hat j\\ \vec b =\(-13.0\ut{m} \)\hat i + \(7.0\ut{m} \)\hat j\\ \end{cases} $$
(a)$\vec a + \vec b=?$ $$ \begin{aligned} \vec a+\vec b &=\vec r = \(4.0-13.0 \)\hat i + \(3.0+7.0 \)\hat j\\ &=\(-9 \)\hat i + \(10 \)\hat j \end{aligned} $$
(b)$\abs{\vec r}=?$ $$ \abs{\vec r}=\sqrt{(-9)^2+10^2}=\sqrt{181}\approx13\ut{m} $$
(c)$\theta_r=?$ $$\theta_r=\tan^{-1}\(\frac{10}{-9}\)\approx 2.3\ut{rad} $$