3-33 할리데이 11판 솔루션 일반물리학

$$ \begin{cases} \vec a&=7.00\ut{m}\i\\ b&=5.00\ut{m},\theta_b=90\degree+35\degree\\ \end{cases} $$ $$ \begin{aligned} \vec b &= 5\cos125\degree\i+5\sin125\degree\j\\ \end{aligned} $$ $$\ab{a,b}$$ $$ \begin{aligned} \vec c &= \vec a+\vec b\\ &=\(7-5 \sin35\degree\)\i+5 \cos35\degree\j\\ \end{aligned} $$ $$\ab{a}$$ $$ \begin{aligned} c&=\sqrt{\(7-5 \sin35\degree\)^2+(5\cos35\degree)^2}\\ &=\sqrt{74-70 \sin35\degree}\ut{m}\\ &\approx 5.818045157561668\ut{m}\\ &\approx 5.82\ut{m}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \theta_c&=\tan ^{-1}\frac{5 \cos35\degree}{7-5 \sin35\degree}\\ &\approx 0.7809793618562755\ut{rad}\\ &\approx 0.781\ut{rad}\\ \end{aligned} $$ $$\ab{c,d}$$ $$ \begin{aligned} \vec d &= \vec b-\vec a\\ &=\(-7-5 \sin35\degree\)\i+5 \cos35\degree\j\\ \end{aligned} $$ $$\ab{c}$$ $$ \begin{aligned} c&=\sqrt{\(-7-5 \sin35\degree\)^2+(5\cos35\degree)^2}\\ &=\sqrt{74+70 \sin35\degree}\ut{m}\\ &\approx 10.6841167414332\ut{m}\\ &\approx 10.7\ut{m}\\ \end{aligned} $$ $$\ab{b}$$ $$ \begin{aligned} \theta_c&=\tan ^{-1}\frac{5 \cos35\degree}{-7-5 \sin35\degree}\\ &\approx 2.748171564069984\ut{rad}\\ &\approx 2.75\ut{rad}\\ \end{aligned} $$