Matematica avancaçada-30

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88. Calcule o produto vetorial entre os vetores \(h = \langle -2, 3, 1 \rangle\) e \(i = \langle 
4, -6, 2 \rangle\). 
 - Resposta: \(h \times i = \langle 0, 0, 0 \rangle\). Explicação: O produto vetorial de dois 
vetores é zero se eles forem paralelos. 
 
89. Resolva a equação \(\frac{1}{2}\sin(5x) + \frac{\sqrt{3}}{2}\cos(5x) = 0\) no intervalo \([0, 
2\pi]\). 
 - Resposta: \(x = \frac{\pi}{30}, \frac{11\pi}{30}, \frac{13\pi}{30}, \frac{17\pi}{30}, 
\frac{19\pi}{30}, \frac{29\pi}{30}, \frac{31\pi}{30}, \frac{41\pi}{30}, \frac{43\pi}{30}, 
\frac{47\pi}{30}, \frac{49\pi}{30}, \frac{59\pi}{30}, \frac{61\pi}{30}, \frac{67\pi}{30}, 
\frac{71\pi}{30}, \frac{73\pi}{30}, \frac{77\pi}{30}, \frac{79\pi}{30}, \frac{89\pi}{30}, 
\frac{91\pi}{30}, \frac{97\pi}{30}, \frac{101\pi}{30}, \frac{103\pi}{30}, \frac{107\pi}{30}, 
\frac{109\pi}{30}, \frac{113\pi}{30}, \frac{121\pi}{30}, \frac{127\pi}{30}, \frac{131\pi}{30}, 
\frac{137\pi}{30}, \frac{139\pi}{30}, \frac{143\pi}{30}, \frac{149\pi}{30}, \frac{151\pi}{30}, 
\frac{157\pi}{30}, \frac{163\pi}{30}, \frac{167\pi}{30}, \frac{169\pi}{30}, \frac{173\pi}{30}, 
\frac{179\pi}{30}, \frac{181\pi}{30}, \frac{191\pi}{30}, \frac{193\pi}{30}, \frac{197\pi}{30}, 
\frac{199\pi}{30}, \frac{211\pi}{30}, \frac{223\pi}{30}, \frac{227\pi}{30}, \frac{229\pi}{30}, 
\frac{233\pi}{30}, \frac{239\pi}{30}, \frac{241\pi}{30}, \frac{251\pi}{30}, \frac{257\pi}{30}, 
\frac{263\pi}{30}, \frac{269\pi}{30}, \frac{271\pi}{30}, \frac{277\pi}{30}, \frac{281\pi}{30}, 
\frac{283\pi}{30}, \frac{293\pi}{30}, \frac{307\pi}{30}, \frac{311\pi}{30}, \frac{313\pi}{30}, 
\frac{317\pi}{30}, \frac{331\pi}{30}, \frac{347\pi}{30}, \frac{349\pi}{30}, \frac{353\pi}{30}, 
\frac{359\pi}{30}, \frac{367\pi}{30}, \frac{373\pi}{30}, \frac{379\pi}{30}, \frac{383\pi}{30}, 
\frac{389\pi}{30}, \frac{397\pi}{30}, \frac{401\pi}{30}, \frac{409\pi}{30}, \frac{419\pi}{30}, 
\frac{421\pi}{30}, \frac{431\pi}{30}, \frac{433\pi}{30}, \frac{439\pi}{30}, \frac{443\pi}{30}, 
\frac{449\pi}{30}, \frac{457\pi}{30}, \frac{461\pi}{30}, \frac{463\pi}{30}, \frac{467\pi}{30}, 
\frac{479\pi}{30}, \frac{487\pi}{30}, \frac{491\pi}{30}, \frac{499\pi}{30}, \frac{503\pi}{30}, 
\frac{509\pi}{30}, \frac{521\pi}{30}, \frac{523\pi}{30}, \frac{541\pi}{30}, \frac{547\pi}{30}, 
\frac{557\pi}{30}, \frac{563\pi}{30}, \frac{569\pi}{30}, \frac{571\pi}{30}, \frac{577\pi}{30}, 
\frac{587\pi}{30}, \frac{593\pi}{30}, \frac{599\pi}{30}, \frac{601\pi}{30}, \frac{607\pi}{30}, 
\frac{613\pi}{30}, \frac{617\pi}{30}, \frac{619\pi}{30}, \frac{631\pi}{30}, \frac{641\pi}{30}, 
\frac{643\pi}{30}, \frac{647\pi}{30}, \frac{653\pi}{30}, \frac{659\pi}{30}, \frac{661\pi}{30}, 
\frac{673\pi}{30}, \frac{677\pi}{30}, \frac{683\pi}{30}, \frac{691\pi}{30}, \frac{701\pi}{30}, 
\frac{709\pi}{30}, \frac{719\pi}{30}, \frac{727\pi}{30}, \frac{733\pi}{30}, \frac{739\pi}{30}, 
\frac{743\pi}{30}, \frac{751\pi}{30}, \frac{757\pi}{30}, \frac{761\pi}{30}, \frac{769\pi}{30}, 
\frac{773\pi}{30}, \frac{787\pi}{30}, \frac{797\pi}{30}, \frac{809\pi}{30}, \frac{811\pi}{30}, 
\frac{821\pi}{30}, \frac{823\pi}{30}, \frac{827\pi}{30}, \frac{829\pi}{30}, 
 
 \frac{839\pi}{30}, \frac{853\pi}{30}, \frac{857\pi}{30}, \frac{859\pi}{30}, \frac{863\pi}{30}, 
\frac{877\pi}{30}, \frac{881\pi}{30}, \frac{883\pi}{30}, \frac{887\pi}{30}, \frac{907\pi}{30}, 
\frac{911\pi}{30}, \frac{919\pi}{30}, \frac{929\pi}{30}, \frac{937\pi}{30}, \frac{941\pi}{30}, 
\frac{947\pi}{30}, \frac{953\pi}{30}, \frac{967\pi}{30}, \frac{971\pi}{30}, \frac{977\pi}{30}, 
\frac{983\pi}{30}, \frac{991\pi}{30}, \frac{997\pi}{30}\). Explicação: Isso ocorre porque 
\(\sin(\frac{\pi}{30}) = \sin(\frac{11\pi}{30}) = \sin(\frac{13\pi}{30}) = \sin(\frac{17\pi}{30}) = 
\sin(\frac{19\pi}{30}) = \sin(\frac{29\pi}{30}) = \sin(\frac{31\pi}{30}) = \sin(\frac{41\pi}{30}) = 
\sin(\frac{43\pi}{30}) = \sin(\frac{47\pi}{30}) = \sin(\frac{49\pi}{30}) = \sin(\frac{59\pi}{30}) =