3-21 할리데이 10판 솔루션 일반물리학

$$\begin{cases} \vec a = 30.0\hat i + 40.0\hat j\\ \vec b = b_x\hat i + (-70.0)\hat j\\ \vec c = (-20.0)\hat i + c_y\hat j\\ \vec d = (-80.0)\hat i + (-70.0)\hat j\\ \vec r = (-140)\hat i + (-20.0)\hat j\\ \end{cases}$$
(a)$b_x=?$ $$30.0+b_x+(-20.0)+(-80.0)=(-140)$$ $$b_x=-70.0$$
(b)$c_y=?$ $$40.0+(-70.0)+c_y+(-70.0)=(-20.0)$$ $$c=80.0$$
(c)$r=?$ $$\begin{aligned} r&=\sqrt{(-140)^2+(-20.0)^2}\\ &=100\sqrt2\\ &\approx 5.2\ut{m}\\ \end{aligned}$$
(b)$\theta_b=?$ $$\begin{aligned} \theta_b&=\tan^{-1}\(\frac{-20.0}{-140}\)\\ &\approx -3.00\ut{rad} \end{aligned}$$