Vecteurs, droites et plans de l’espace - Spécialité

Section

Exercice 1 : Nature de la section d'un solide par un plan

Parmi les propositions ci-dessous, sélectionner celles dont la section est un rectangle :

A. la section d'un pavé droit par un plan parallèle à une face
B. la section d'un cône de révolution par un plan parallèle à sa base
C. la section d'un cylindre par un plan parallèle à l'axe de révolution
D. la section d'un cylindre par un plan parallèle aux bases

Exercice 2 : Tracer une section d'un solide par un plan

Tracer l'intersection du cube ABCDEFGH avec le plan (IJK).

I est le milieu de [EF].
J est le milieu de [BF].
K est le milieu de [CD].

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[20.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 7.0], [20.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 8.0], [20.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 9.0], [20.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 10.0], [20.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 11.0], [20.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 12.0], [20.0, 12.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 13.0], [20.0, 13.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 14.0], [20.0, 14.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 15.0], [20.0, 15.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 16.0], [20.0, 16.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 17.0], [20.0, 17.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 18.0], [20.0, 18.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 19.0], [20.0, 19.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 20.0], [20.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, -20.0], [-20.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-19.0, -20.0], [-19.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-18.0, -20.0], [-18.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-17.0, -20.0], [-17.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-16.0, -20.0], [-16.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-15.0, -20.0], [-15.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-14.0, -20.0], [-14.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-13.0, -20.0], [-13.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-12.0, -20.0], [-12.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-11.0, -20.0], [-11.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -20.0], [-10.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -20.0], [-9.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -20.0], [-8.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -20.0], [-7.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -20.0], [-6.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -20.0], [-5.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -20.0], [-4.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-3.0, -20.0], [-3.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-2.0, -20.0], [-2.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-1.0, -20.0], [-1.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, -20.0], [0.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, -20.0], [1.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, -20.0], [2.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, -20.0], [3.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, -20.0], [4.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[5.0, -20.0], [5.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, -20.0], [6.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[7.0, -20.0], [7.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[8.0, -20.0], [8.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[9.0, -20.0], [9.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[10.0, -20.0], [10.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[11.0, -20.0], [11.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[12.0, -20.0], [12.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[13.0, -20.0], [13.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[14.0, -20.0], [14.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[15.0, -20.0], [15.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[16.0, -20.0], [16.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[17.0, -20.0], [17.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[18.0, -20.0], [18.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[19.0, -20.0], [19.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[20.0, -20.0], [20.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -8.0], [-8.0, 8.0], {"subtype": "segment"}], [[-8.0, 8.0], [8.0, 8.0], {"subtype": "segment"}], [[8.0, 8.0], [8.0, -8.0], {"subtype": "segment"}], [[8.0, -8.0], [-8.0, -8.0], {"subtype": "segment"}], [[-4.0, -4.0], [-4.0, 12.0], {"subtype": "segment", "stroke-dasharray": "- "}], [[-4.0, 12.0], [12.0, 12.0], {"subtype": "segment"}], [[12.0, 12.0], [12.0, -4.0], {"subtype": "segment"}], [[12.0, -4.0], [-4.0, -4.0], {"subtype": "segment", "stroke-dasharray": "- "}], [[-8.0, -8.0], [-4.0, -4.0], {"subtype": "segment", "stroke-dasharray": "- "}], [[-8.0, 8.0], [-4.0, 12.0], {"subtype": "segment"}], [[8.0, 8.0], [12.0, 12.0], {"subtype": "segment"}], [[8.0, -8.0], [12.0, -4.0], {"subtype": "segment"}]], "label": [[[-8.0, -8.0], "A", "below left", {}], [[-8.0, 8.0], "B", "above left", {}], [[8.0, 8.0], "C", "above right", {}], [[8.0, -8.0], "D", "below right", {}], [[-4.0, -4.0], "E", "below left", {}], [[-4.0, 12.0], "F", "above left", {}], [[12.0, 12.0], "G", "above right", {}], [[12.0, -4.0], "H", "below right", {}], [[-4.0, 4.0], "I", "above left", {"color": "#0000ff"}], [[-6.0, 10.0], "J", "above left", {"color": "#0000ff"}], [[8.0, 0.0], "K", "right", {"color": "#0000ff"}]], "circle": [[[-4.0, 4.0], 0.2, {"fill": "#0000ff", "stroke": "#0000ff"}], [[-6.0, 10.0], 0.2, {"fill": "#0000ff", "stroke": "#0000ff"}], [[8.0, 0.0], 0.2, {"fill": "#0000ff", "stroke": "#0000ff"}]], "drawing_options": {"tools": ["segment", "no_construction"]}}

Exercice 3 : Nature de la section d'un solide par un plan

Parmi les propositions ci-dessous, sélectionner celles dont la section est un rectangle :

A. la section d'une sphère par un plan
B. la section d'un cylindre par un plan parallèle aux bases
C. la section d'un pavé droit par un plan parallèle à une arête
D. la section d'un cône de révolution par un plan parallèle à sa base

Exercice 4 : Tracer une section d'un solide par un plan

Tracer l'intersection du cube ABCDEFGH avec le plan (IJK).

I est le milieu de [CG].
J est le milieu de [CD].
K est le milieu de [AE].

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[20.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 7.0], [20.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 8.0], [20.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 9.0], [20.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 10.0], [20.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 11.0], [20.0, 11.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 12.0], [20.0, 12.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 13.0], [20.0, 13.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 14.0], [20.0, 14.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 15.0], [20.0, 15.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 16.0], [20.0, 16.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 17.0], [20.0, 17.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 18.0], [20.0, 18.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 19.0], [20.0, 19.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, 20.0], [20.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-20.0, -20.0], [-20.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-19.0, -20.0], [-19.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-18.0, -20.0], [-18.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-17.0, -20.0], [-17.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-16.0, -20.0], [-16.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-15.0, -20.0], [-15.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-14.0, -20.0], [-14.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-13.0, -20.0], [-13.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-12.0, -20.0], [-12.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-11.0, -20.0], [-11.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-10.0, -20.0], [-10.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-9.0, -20.0], [-9.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -20.0], [-8.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -20.0], [-7.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -20.0], [-6.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -20.0], [-5.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -20.0], [-4.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-3.0, -20.0], [-3.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-2.0, -20.0], [-2.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-1.0, -20.0], [-1.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, -20.0], [0.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, -20.0], [1.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, -20.0], [2.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, -20.0], [3.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, -20.0], [4.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[5.0, -20.0], [5.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, -20.0], [6.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[7.0, -20.0], [7.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[8.0, -20.0], [8.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[9.0, -20.0], [9.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[10.0, -20.0], [10.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[11.0, -20.0], [11.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[12.0, -20.0], [12.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[13.0, -20.0], [13.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[14.0, -20.0], [14.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[15.0, -20.0], [15.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[16.0, -20.0], [16.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[17.0, -20.0], [17.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[18.0, -20.0], [18.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[19.0, -20.0], [19.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[20.0, -20.0], [20.0, 20.0], {"subtype": "segment", "stroke": "#ccc"}], [[-8.0, -8.0], [-8.0, 8.0], {"subtype": "segment"}], [[-8.0, 8.0], [8.0, 8.0], {"subtype": "segment"}], [[8.0, 8.0], [8.0, -8.0], {"subtype": "segment"}], [[8.0, -8.0], [-8.0, -8.0], {"subtype": "segment"}], [[-4.0, -4.0], [-4.0, 12.0], {"subtype": "segment", "stroke-dasharray": "- "}], [[-4.0, 12.0], [12.0, 12.0], {"subtype": "segment"}], [[12.0, 12.0], [12.0, -4.0], {"subtype": "segment"}], [[12.0, -4.0], [-4.0, -4.0], {"subtype": "segment", "stroke-dasharray": "- "}], [[-8.0, -8.0], [-4.0, -4.0], {"subtype": "segment", "stroke-dasharray": "- "}], [[-8.0, 8.0], [-4.0, 12.0], {"subtype": "segment"}], [[8.0, 8.0], [12.0, 12.0], {"subtype": "segment"}], [[8.0, -8.0], [12.0, -4.0], {"subtype": "segment"}]], "label": [[[-8.0, -8.0], "A", "below left", {}], [[-8.0, 8.0], "B", "above left", {}], [[8.0, 8.0], "C", "above right", {}], [[8.0, -8.0], "D", "below right", {}], [[-4.0, -4.0], "E", "below left", {}], [[-4.0, 12.0], "F", "above left", {}], [[12.0, 12.0], "G", "above right", {}], [[12.0, -4.0], "H", "below right", {}], [[10.0, 10.0], "I", "above right", {"color": "#0000ff"}], [[8.0, 0.0], "J", "right", {"color": "#0000ff"}], [[-6.0, -6.0], "K", "below left", {"color": "#0000ff"}]], "circle": [[[10.0, 10.0], 0.2, {"fill": "#0000ff", "stroke": "#0000ff"}], [[8.0, 0.0], 0.2, {"fill": "#0000ff", "stroke": "#0000ff"}], [[-6.0, -6.0], 0.2, {"fill": "#0000ff", "stroke": "#0000ff"}]], "drawing_options": {"tools": ["segment", "no_construction"]}}

Exercice 5 : Nature de la section d'un solide par un plan

Parmi les propositions ci-dessous, sélectionner celles dont la section est un cercle ou un disque :

A. la section d'un pavé droit par un plan parallèle à une arête
B. la section d'une sphère par un plan
C. la section d'un pavé droit par un plan parallèle à une face
D. la section d'un cylindre par un plan parallèle aux bases

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