10판/3. 벡터

3-7 할리데이 10판 솔루션 일반물리학

짱세디럭스 2019. 8. 6. 17:34

{a:(3[m],θa)b:(4[m],θb)θaθb=ϕ\begin{cases} \vec a:(3\ut{m},\theta_a)\\ \vec b:(4\ut{m},\theta_b)\\ \theta_a-\theta_b=\phi \end{cases} {a=3cosθai^+3sinθaj^b=4cosθbi^+4sinθbj^\begin{cases} \vec a = 3\cos\theta_a\hat i+3\sin\theta_a\hat j\\ \vec b = 4\cos\theta_b\hat i+4\sin\theta_b\hat j\\ \end{cases} a+b=(3cosθa+4cosθb)i^+(3sinθa+4sinθb)j^\vec a+\vec b = \(3\cos\theta_a+4\cos\theta_b\)\hat i+\(3\sin\theta_a+4\sin\theta_b\)\hat j a+b=(3cosθa+4cosθb)2+(3sinθa+4sinθb)2=25+24cos(θaθb)=25+24cosϕ \begin{aligned} \abs{\vec a+\vec b} &= \sqrt{\(3\cos\theta_a+4\cos\theta_b\)^2+\(3\sin\theta_a+4\sin\theta_b\)^2}\\ &=\sqrt{25+24\cos\(\theta_a-\theta_b\)}\\ &=\sqrt{25+24\cos\phi}\\ \end{aligned}
(a)7m 7=25+24cosϕa 7 =\sqrt{25+24\cos\phi_a} ϕa=0 \phi_a = 0
(b)1m 1=25+24cosϕb 1 =\sqrt{25+24\cos\phi_b} ϕb=±π \phi_b = \pm \pi
(c)5m 5=25+24cosϕc 5 =\sqrt{25+24\cos\phi_c} ϕc=±π2 \phi_c = \pm \frac{\pi}{2}