Quiz — 08 - Repérage dans l'espace .pdf

Question 1 sur 10 20:00

[{"id":40230,"question":"Quel est le repère orthonormé standard en 3D ?","option_a":"(O, i, j)","option_b":"(O, i, j, k)","option_c":"(O, x, y, z)","option_d":"(O, u, v, w)","option_e":"","option_f":"","bonne_reponse":"b","explication":"Le repère orthonormé standard en 3D est (O, i, j, k), où i, j et k sont des vecteurs unitaires orthogonaux.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"(O, i, j)\", \"b\": \"(O, i, j, k)\", \"c\": \"(O, x, y, z)\", \"d\": \"(O, u","_debug_options_count":4},{"id":40231,"question":"Vrai ou Faux ? Les coordonnées d'un point dans l'espace sont toujours positives.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Faux. Les coordonnées d'un point peuvent être négatives, positives ou nulles selon sa position dans l'espace.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":40232,"question":"Quelle est la formule du milieu M d'un segment [AB] dans l'espace ?","option_a":"M = (A + B)\/2","option_b":"M = (A - B)\/2","option_c":"M = (xA + xB, yA + yB)","option_d":"M = (xA - xB, yA - yB)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le milieu M d'un segment [AB] a pour coordonnées ( (xA + xB)\/2 , (yA + yB)\/2 , (zA + zB)\/2 ).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"M = (A + B)\/2\", \"b\": \"M = (A - B)\/2\", \"c\": \"M = (xA + xB, yA + yB","_debug_options_count":4},{"id":40233,"question":"Vrai ou Faux ? Deux vecteurs colinéaires ont toujours la même direction.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai. Deux vecteurs colinéaires sont des vecteurs qui ont la même direction ou des directions opposées.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":40234,"question":"Quel est le vecteur directeur de la droite passant par les points A(1, 2, 3) et B(4, 5, 6) ?","option_a":"AB = (3, 3, 3)","option_b":"AB = (5, 7, 9)","option_c":"AB = (-3, -3, -3)","option_d":"AB = (1, 2, 3)","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le vecteur directeur AB est obtenu en soustrayant les coordonnées de A à celles de B : AB = (4-1, 5-2, 6-3) = (3, 3, 3).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"AB = (3, 3, 3)\", \"b\": \"AB = (5, 7, 9)\", \"c\": \"AB = (-3, -3, -3)\",","_debug_options_count":4},{"id":40235,"question":"Vrai ou Faux ? La norme d'un vecteur est toujours positive.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai. La norme d'un vecteur, qui représente sa longueur, est toujours un nombre positif ou nul.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":40236,"question":"Quelle est la distance entre les points A(1, 0, 2) et B(4, 3, 6) ?","option_a":"√(22)","option_b":"√(34)","option_c":"5","option_d":"√(14)","option_e":"","option_f":"","bonne_reponse":"b","explication":"La distance est calculée par √[(4-1)² + (3-0)² + (6-2)²] = √(9 + 9 + 16) = √34.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"√(22)\", \"b\": \"√(34)\", \"c\": \"5\", \"d\": \"√(14)\"}}","_debug_options_count":4},{"id":40237,"question":"Vrai ou Faux ? Un vecteur nul a une norme égale à 1.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"b","explication":"Faux. Un vecteur nul a une norme égale à 0, car il n'a ni direction ni longueur.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"b\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4},{"id":40238,"question":"Quel est le produit scalaire de deux vecteurs orthogonaux ?","option_a":"0","option_b":"1","option_c":"Leur norme","option_d":"Indéfini","option_e":"","option_f":"","bonne_reponse":"a","explication":"Le produit scalaire de deux vecteurs orthogonaux est toujours égal à 0, car cos(90°) = 0.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"0\", \"b\": \"1\", \"c\": \"Leur norme\", \"d\": \"Indéfini\"}}","_debug_options_count":4},{"id":40239,"question":"Vrai ou Faux ? Les coordonnées d'un vecteur sont indépendantes de l'origine du repère.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"a","explication":"Vrai. Les coordonnées d'un vecteur représentent ses composantes, qui ne dépendent pas de l'origine du repère.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0,"_debug_answer_data_type":"string","_debug_answer_data_preview":"{\"correct\": \"a\", \"options\": {\"a\": \"Vrai\", \"b\": \"Faux\", \"c\": \"\", \"d\": \"\"}}","_debug_options_count":4}]