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{"version":3,"file":"2G33-2-tx0VQ0zk.js","sources":["../../src/exercices/2e/2G33-2.js"],"sourcesContent":["import { combinaisonListes } from '../../lib/outils/arrayOutils'\nimport { ecritureAlgebrique, ecritureParentheseSiNegatif, reduireAxPlusB } from '../../lib/outils/ecritures'\nimport Exercice from '../deprecatedExercice.js'\n\nimport { listeQuestionsToContenu, randint } from '../../modules/outils.js'\nexport const titre = 'Determine if lines are parallel, intersecting or coincident'\n\n/**\n * Description didactique de l'exercice\n * @author Stéphane Guyon\n * Référence 2G33-2, ex 2G50-2\n*/\nexport const uuid = 'e715d'\nexport const ref = '2G33-2'\nexport default function PositionsDeDroites () {\n Exercice.call(this) // Héritage de la classe Exercice()\n this.titre = titre\n this.consigne = 'Determine whether the lines $\\\\bm{(d)}$ and $\\\\bm{(d\\')}$, of which the Cartesian equations are given below, are parallel, coincident or secant.'\n this.nbQuestions = 3\n this.nbCols = 2 // Uniquement pour la sortie LaTeX\n this.nbColsCorr = 2 // Uniquement pour la sortie LaTeX\n this.sup = 1 // Niveau de difficulté\n this.tailleDiaporama = 2 // Pour les exercices chronométrés. 50 par défaut pour les exercices avec du texte\n this.video = '' // Id YouTube ou url\n\n const typeQuestionsDisponibles = ['type1', 'type1', 'type2'] //, 'type1', 'type2' On créé 2 types de questions\n const listeTypeQuestions = combinaisonListes(typeQuestionsDisponibles, this.nbQuestions) // Tous les types de questions sont posés mais l'ordre diffère à chaque 'cycle'\n this.nouvelleVersion = function () {\n this.listeQuestions = [] // Liste de questions\n this.listeCorrections = [] // Liste de questions corrigées\n\n for (let i = 0, a1, b1, c1, k, a2, b2, c2, texte, texteCorr, cpt = 0; i < this.nbQuestions && cpt < 50;) {\n // Main loop where i+1 corresponds to the question number\n switch (listeTypeQuestions[i]) { // Suivant le type de question, le contenu sera différent\n case 'type1':\n a1 = randint(-9, 9, 0)\n b1 = randint(-9, 9, 0)\n c1 = randint(-9, 9)\n a2 = randint(-9, 9, 0)\n b2 = randint(-9, 9, 0)\n c2 = randint(-9, 9)\n\n texte = 'We give: $(d): '\n if (a1 !== 0) {\n texte += `${reduireAxPlusB(a1, 0)}`\n }\n if (b1 === 1) { // cas où b=1\n texte += '+ y'\n }\n if (b1 === -1) { // cas où b=1\n texte += '-y'\n }\n if (b1 !== 1 & b1 !== 0 & b1 !== -1) { // cas général\n texte += `${ecritureAlgebrique(b1)} y`\n }\n if (c1 !== 0) {\n texte += `${ecritureAlgebrique(c1)}`\n }\n texte += '=0$'\n texte += ' and $(d\\') : '\n if (a2 !== 0) {\n texte += `${reduireAxPlusB(a2, 0)}`\n }\n if (b2 === 1) { // cas où b=1\n texte += '+ y'\n }\n if (b2 === -1) { // cas où b=1\n texte += '-y'\n }\n if (b2 !== 1 & b2 !== 0 & b2 !== -1) { // cas général\n texte += `${ecritureAlgebrique(b2)} y`\n }\n if (c2 !== 0) {\n texte += `${ecritureAlgebrique(c2)}`\n }\n texte += '=0$'\n\n texteCorr = 'We know that a line $(d)$ with a Cartesian equation: '\n texteCorr += ' $(d): ax+by+c=0$, with $(a,b)\\\\neq (0,0)$.'\n texteCorr += '<br>admits a direction vector of coordinates: '\n texteCorr += '$\\\\vec {u} \\\\begin{pmatrix}-b\\\\\\\\a\\\\end{pmatrix}$.'\n texteCorr += `<br>As we have from the statement: $a=${a1}$ , $b=${b1}$ , $c=${c1}$ ,`\n texteCorr += 'we deduce that: $\\\\vec {u} \\\\begin{pmatrix}'\n if (b1 === 0) { texteCorr += '0' } else { texteCorr += `-${ecritureParentheseSiNegatif(b1)}` }\n texteCorr += `\\\\\\\\${a1}\\\\end{pmatrix}$ is a direction vector of $(d)$. `\n texteCorr += `<br>Similarly, let $\\\\vec {u'}$ be the direction vector of $(d')$. <br>As here, we have: $a=${a2}$ , $b=${b2}$ , $c=${c2}$ ,`\n texteCorr += 'we deduce that: $\\\\vec {u\\'} \\\\begin{pmatrix}'\n if (b2 === 0) { texteCorr += '0' } else { texteCorr += `-${ecritureParentheseSiNegatif(b2)}` }\n texteCorr += `\\\\\\\\${a2}\\\\end{pmatrix}$`\n texteCorr += '<br> To determine the relative position of $(d)$ and $(d\\')$, we study the collinearity of the two direction vectors. '\n texteCorr += '<br> To do this, we calculate their determinant: '\n texteCorr += `$Det\\\\big(\\\\vec u,\\\\vec {u'}\\\\big)=\\\\begin{vmatrix}${-b1}&${-b2}\\\\\\\\${a1}&${a2}\\\\end{vmatrix}=${ecritureParentheseSiNegatif(-b1)} \\\\times ${ecritureParentheseSiNegatif(a2)} - ${ecritureParentheseSiNegatif(a1)} \\\\times ${ecritureParentheseSiNegatif(-b2)}=${-b1 * a2 + a1 * b2}$`\n if (-b1 * a2 + a1 * b2 !== 0) {\n texteCorr += '<br>We observe that the determinant is non-zero. <br>The direction vectors of the two lines are therefore not collinear.'\n texteCorr += '<br>The lines $(d)$ and $(d\\')$ ne sont donc pas parallèles.'\n } else {\n texteCorr += '<br>We observe that the determinant is zero. <br>The direction vectors of the two lines are therefore collinear.'\n texteCorr += '<br>The lines $(d)$ and $(d\\')$ are then parallel.'\n }\n if (a1 * b2 === a2 * b1 & a1 * c1 === a2 * c2 & b1 * c2 === b2 * c1) {\n texteCorr += 'We even observe that in this situation, the equations being multiples of each other, the two lines are confused.'\n }\n break\n case 'type2':\n a1 = randint(-9, 9, 0)\n b1 = randint(-9, 5, 0)\n c1 = randint(-5, 5)\n k = randint(-9, 9, [0, 1])\n a2 = a1 * k\n b2 = b1 * k\n c2 = randint(-7, 7)\n\n texte = 'We give: $(d): '\n if (a1 !== 0) {\n texte += `${reduireAxPlusB(a1, 0)}`\n }\n if (b1 === 1) { // cas où b=1\n texte += '+ y'\n }\n if (b1 === -1) { // cas où b=1\n texte += '-y'\n }\n if (b1 !== 1 & b1 !== 0 & b1 !== -1) { // cas général\n texte += `${ecritureAlgebrique(b1)} y`\n }\n if (c1 !== 0) {\n texte += `${ecritureAlgebrique(c1)}`\n }\n texte += '=0$'\n texte += ' and $(d\\') : '\n if (a2 !== 0) {\n texte += `${reduireAxPlusB(a2, 0)}`\n }\n if (b2 === 1) { // cas où b=1\n texte += '+ y'\n }\n if (b2 === -1) { // cas où b=1\n texte += '-y'\n }\n if (b2 !== 1 & b2 !== 0 & b2 !== -1) { // cas général\n texte += `${ecritureAlgebrique(b2)} y`\n }\n if (c2 !== 0) {\n texte += `${ecritureAlgebrique(c2)}`\n }\n texte += '=0$'\n\n texteCorr = 'We know that a right-hand Cartesian equation of the form: '\n texteCorr += '$(d): ax+by+c=0$, with $(a,b)\\\\neq (0,0)$.'\n texteCorr += '<br>admits a direction vector of coordinates: '\n texteCorr += '$\\\\vec {u} \\\\begin{pmatrix}-b\\\\\\\\a\\\\end{pmatrix}$.'\n texteCorr += '<br>Let $\\\\vec {u}$ be the direction vector of $(d)$: '\n texteCorr += `<br>As we have according to the statement: $a=${a1}$, $b=${b1}$, $c=${c1}$`\n texteCorr += ', we deduce that: $\\\\vec {u} \\\\begin{pmatrix}'\n if (b1 === 0) { texteCorr += '0' } else { texteCorr += `-${ecritureParentheseSiNegatif(b1)}` }\n texteCorr += `\\\\\\\\${a1}\\\\end{pmatrix}$`\n texteCorr += `<br>Similarly for $(d')$: $a=${a2}$, $b=${b2}$, $c=${c2}$`\n texteCorr += ', we deduce that: $\\\\vec {u\\'} \\\\begin{pmatrix}'\n if (b2 === 0) { texteCorr += '0' } else { texteCorr += `-${ecritureParentheseSiNegatif(b2)}` }\n texteCorr += `\\\\\\\\${a2}\\\\end{pmatrix}$`\n texteCorr += '<br> To determine the relative position of $(d)$ and $(d\\')$, we study the collinearity of the two direction vectors. '\n texteCorr += '<br> To do this, we calculate their determinant: '\n texteCorr += `$Det\\\\big(\\\\vec u,\\\\vec {u'}\\\\big)=\\\\begin{vmatrix}${-b1}&${-b2}\\\\\\\\${a1}&${a2}\\\\end{vmatrix}=${ecritureParentheseSiNegatif(-b1)} \\\\times ${ecritureParentheseSiNegatif(a2)} - ${ecritureParentheseSiNegatif(a1)} \\\\times ${ecritureParentheseSiNegatif(-b2)}=${-b1 * a2 + a1 * b2}$`\n if (-b1 * a2 + a1 * b2 !== 0) {\n texteCorr += '<br>We observe that the determinant is non-zero. <br>The direction vectors of the two lines are therefore not collinear.'\n texteCorr += '<br>The lines $(d)$ and $(d\\')$ ne sont donc pas parallèles.'\n } else {\n texteCorr += '<br>We observe that the determinant is zero. <br>The direction vectors of the two lines are therefore collinear.'\n texteCorr += '<br>The lines $(d)$ and $(d\\')$ are then parallel.'\n }\n if (a1 * b2 === a2 * b1 & a1 * c1 === a2 * c2 & b1 * c2 === b2 * c1) {\n texteCorr += '<br>We even observe that in this situation, the equations being 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