{"id":181502,"date":"2023-03-10T19:48:47","date_gmt":"2023-03-10T18:48:47","guid":{"rendered":"https:\/\/groupe-reussite.fr\/ressources\/?page_id=181502"},"modified":"2023-03-10T19:58:39","modified_gmt":"2023-03-10T18:58:39","slug":"cours-en-ligne-exercices-corriges-geometrie-terminale-d","status":"publish","type":"page","link":"https:\/\/groupe-reussite.fr\/ressources\/cours-en-ligne-exercices-corriges-geometrie-terminale-d\/","title":{"rendered":"Exercices et corrig\u00e9s g\u00e9om\u00e9trie dans l’espace terminale D"},"content":{"rendered":"
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Cours en ligne Terminale D en maths<\/a><\/p>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Chapitres de maths en Terminale D<\/p>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Exercices et corrig\u00e9s sur la g\u00e9om\u00e9trie dans l’espace en Terminale D<\/h1>\n<\/div>\n

R\u00e9sum\u00e9 de cours<\/a> Exercices et corrig\u00e9s<\/a><\/p>\n

Cours en ligne de maths en Terminale D<\/a><\/p>\n

Vous trouverez ci-dessous des exercices corrig\u00e9s gratuits sur la g\u00e9om\u00e9trie dans l’espace pour les \u00e9l\u00e8ves pr\u00e9parant le bac D.<\/p>\n

QCM sur la g\u00e9om\u00e9trie dans l’espace en terminale D<\/h2>\n

Dans le rep\u00e8re \"(O,\overrightarrow{i}, \overrightarrow{j},\overrightarrow{k})\" de l’espace, on consid\u00e8re les points \"A(0;-5;0)\", \"B(1;0;1)\", \"C(-1;-7;0)\"; la droite \"D\" d’\u00e9quation param\u00e9trique: \"\left\{
\net le plan \"P\" d’\u00e9quation: \"3x-2y-10=0.\"<\/p>\n

Question 1 :<\/strong><\/p>\n

Le point \"A\":<\/p>\n

a. appartient \u00e0 \"D\" et \u00e0 \"P\"<\/p>\n

b. appartient \u00e0 \"D\" mais pas \u00e0 \"P\"<\/p>\n

c. appartient \u00e0 \"P\" et \u00e0 \"D\"<\/p>\n

Question 2 :<\/strong><\/p>\n

Le triangle \"ABC\" est:<\/p>\n

a. rectangle en \"A\"<\/p>\n

b. rectangle en \"B\"<\/p>\n

c. rectangle en \"C\"<\/p>\n

d. aucune des trois proposition ci-dessus n’est correcte.<\/p>\n

Question 3 :<\/strong><\/p>\n

\"D\" et \"P\" sont:<\/p>\n

a. parall\u00e8les<\/p>\n

b. s\u00e9cantes non perpendiculaires.<\/p>\n

c. perpendiculaires<\/p>\n

d. aucune des trois proposition ci-dessus n’est correcte.<\/p>\n

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COURS DE MATHS<\/h3>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Les meilleurs professeurs particuliers<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Pour progresser et r\u00e9ussir<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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\n\t\t\t\t\t\n\t\t\t\t\t\t\n\t\t\t\t\t\t\t\t\tCours particuliers maths<\/span>\n\t\t\t\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Avis Google France <\/b>\u2605\u2605\u2605\u2605\u2605<\/b><\/span> 4,9 sur 5<\/b><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t

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Corrig\u00e9 du QCM de terminale D g\u00e9om\u00e9trie dans l’espace<\/h2>\n

Question 1 :<\/strong><\/p>\n

Supposons que \"A \in D\"<\/p>\n

Alors il existe un r\u00e9el \"a\" tel que<\/p>\n

\"\left\{<\/p>\n

  <\/span>   <\/span>\"\[\Longleftrightarrow\]\"<\/p>\n

\"\left\{<\/p>\n

  <\/span>   <\/span>\"\[\Longleftrightarrow\]\"<\/p>\n

\"\left\{<\/p>\n

Ce r\u00e9el \"a\" existe, donc on a bien \"A \in D\"<\/p>\n

De plus, on a \"3\times 0 - 2\times (-5) - 10 = 0 + 10 - 10 = 0\"<\/p>\n

Donc les coordonn\u00e9es du point \"A\" v\u00e9rifient l’\u00e9quation du plan \"P\"<\/p>\n

Donc \"A \in P\"<\/p>\n

Donc le point \"A\" appartient \u00e0 \"D\" et \u00e0 \"P\"<\/p>\n

Question 2 :<\/strong><\/p>\n

On a<\/p>\n

\"AB^2 = \sqrt{(1-0)^2+(0-(-5))^2+(1-0)^2}^2\"<\/p>\n

=\"1^2+5^2+1^2=1+25+1=27\"<\/p>\n

\"AC^2 = \sqrt{(-1-0)^2+(-7-(-5))^2+(0-0)^2}^2\"<\/p>\n

=\"(-1)^2+(-2)^2+0^2=1+4+0=5\"<\/p>\n

\"BC^2 = \sqrt{(-1-1)^2+(-7-0)^2+(0-1)^2}^2\"<\/p>\n

=\"(-2)^2+(-7)^2+(-1)^2=4+49+1=54\"<\/p>\n

Donc \"AB^2+AC^2=27+5=32\", \"AB^2+BC^2=27+54=81\" et \"AC^2+BC^2=5+54=59\"<\/p>\n

Donc \"BC^2\neq AB^2+AC^2\", \"AC^2\neq AB^2+BC^2\" et \"AB^2\neq AC^2+BC^2\"<\/p>\n

Donc \"ABC\" n’est pas un triangle rectangle, ni en \"A\", ni en \"B\", ni en \"C\"<\/p>\n

Question 3 :<\/strong><\/p>\n

D’apr\u00e8s sa repr\u00e9sentation param\u00e9trique, le vecteur \"\overrightarrow{u} \begin{pmatrix} est un vecteur normal au plan \"P\"<\/p>\n

D’apr\u00e8s son \u00e9quation cart\u00e9sienne, le vecteur, le vecteur \"\overrightarrow{u} \begin{pmatrix} est un vecteur normal au plan \"P\"<\/p>\n

Supposons que \"\overrightarrow{u}\" et \"\overrightarrow{n}\" soient colin\u00e9aires, alors il existe un r\u00e9el \"k\" tel que<\/p>\n

\"\overrightarrow{u}=k\overrightarrow{n}\"<\/p>\n

Donc \"\left\{\begin{array}{ccc} -6 & = & 3k \\<\/p>\n

\"\Longleftrightarrow \left\{\begin{array}{ccc} donc on a bien \"\overrightarrow{u}=2\overrightarrow{n}\"<\/p>\n

Donc \"\overrightarrow{u}\" et \"\overrightarrow{n}\" sont colin\u00e9aires<\/p>\n

Donc \"D\" et \"P\" sont perpendiculaires<\/p>\n

Exercices g\u00e9om\u00e9trie dans l’espace terminale D<\/h2>\n

Exercice sur la repr\u00e9sentation param\u00e9trique en terminale D<\/h3>\n

On consid\u00e8re les points \"A(2;-3;0)\", \"B(-1;2;4)\", et \"C(-3;3;0)\".<\/p>\n

Donner une repr\u00e9sentation param\u00e9trique de la droite \"(AB)\".<\/p>\n

Exercice sur l’\u00e9quation cart\u00e9sienne du plan<\/h3>\n

D\u00e9terminer une \u00e9quation cart\u00e9sienne du plan \"P\" d\u00e9fini par la condition suivante :<\/p>\n

Le projet\u00e9 orthogonal de l’origine \"O\" sur \"P\" est le point \"A(1;-5;7)\".<\/p>\n

Corrig\u00e9 des exercices g\u00e9om\u00e9trie dans l’espace<\/h2>\n

Corrig\u00e9 de l’exercice repr\u00e9sentation param\u00e9trique<\/h3>\n

La droite \"(AB)\" est l’ensemble des points \"M(x;y;z)\" tels que:<\/p>\n

  <\/span>   <\/span>\"\[\exists k \in \mathbb{R}\text{, }\overrightarrow{AM}=k\overrightarrow{AB}=k\begin{pmatrix}<\/p>\n

  <\/span>   <\/span>\"\[\Longleftrightarrow \exists k \in \mathbb{R}: \left \{<\/p>\n

  <\/span>   <\/span>\"\[\Longleftrightarrow \exists k \in \mathbb{R}: \left \{<\/p>\n

Corrig\u00e9 de l’exercice sur l’\u00e9quation cart\u00e9sienne du plan en terminale D<\/h3>\n

Le vecteur \"\overrightarrow{OA} \begin{pmatrix} est normal au plan \"P\". Une \u00e9quation de \"P\" s’\u00e9crit donc:<\/p>\n

  <\/span>   <\/span>\"\[P\text{ : }x-5y+7z+d=0\text{, avec }d\in \mathbb{R}\]\"<\/p>\n

Le point \"A\" appartient au plan \"P\". Donc \"1 - 5 \times (-5) + 7 \times 7 + d = 0 \Longrightarrow d = -75\".<\/p>\n

Ainsi, une \u00e9quation de \"P\" est finalement:<\/p>\n

\"{P\text{ : }x-5y+7z-75=0\text{, avec }d\in \mathbb{R}\"<\/p>\n

Retrouvez d’autres exercices et corrig\u00e9s des cours de maths niveau terminale D :<\/p>\n

    \n
  • Exercices corrig\u00e9 gratuit : Fonction exponentielle<\/li>\n
  • Exercices corrig\u00e9 gratuit : Equations diff\u00e9rentielles<\/li>\n
  • Exercices corrig\u00e9 gratuit\u00a0 : Statistiques<\/li>\n
  • Exercices corrig\u00e9 gratuit : Exercices probabilit\u00e9<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/section>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

    Exercices et corrig\u00e9s sur la g\u00e9om\u00e9trie dans l’espace en Terminale D R\u00e9sum\u00e9 de cours Exercices et corrig\u00e9s Cours en ligne de maths en Terminale D Vous trouverez ci-dessous des exercices corrig\u00e9s gratuits sur la g\u00e9om\u00e9trie dans l’espace pour les \u00e9l\u00e8ves pr\u00e9parant le bac D. QCM sur la g\u00e9om\u00e9trie dans l’espace en terminale D Dans le 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