Vecteurs - 2de

Somme de vecteurs

Exercice 1 : Exprimer un vecteur en fonction de deux autres vecteurs

Exprimer le vecteur \( \overrightarrow{w} \) en fonction des vecteurs \( \overrightarrow{u} \) et \( \overrightarrow{v} \).

{"init": {"range": [[-1.0, 11.0], [-1.25, 11.0]], "scale": [20, 20]}, "line": [[[0.0, 0.0], [10.0, 0.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 1.0], [10.0, 1.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 2.0], [10.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 3.0], [10.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 4.0], [10.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 5.0], [10.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 6.0], [10.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 7.0], [10.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 8.0], [10.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 9.0], [10.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 10.0], [10.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 0.0], [0.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, 0.0], [1.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, 0.0], [2.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, 0.0], [3.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, 0.0], [4.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[5.0, 0.0], [5.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, 0.0], [6.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[7.0, 0.0], [7.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[8.0, 0.0], [8.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[9.0, 0.0], [9.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[10.0, 0.0], [10.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, 1.0], [1.0, 6.0], {"subtype": "vector", "arrow-end": "classic-wide-long", "stroke": "#0080FF"}], [[1.0, 1.0], [4.0, 1.0], {"subtype": "vector", "arrow-end": "classic-wide-long", "stroke": "#FF0000"}], [[1.0, 1.0], [5.0, 6.0], {"subtype": "vector", "arrow-end": "classic-wide-long", "stroke": "#0000CC"}]], "label": [[[3.5, 3.0], "\\overrightarrow{u}", "center", {"color": "#0080FF"}], [[5.5, 0.0], "\\overrightarrow{v}", "center", {"color": "#FF0000"}], [[5.5, 4.0], "\\overrightarrow{w}", "center", {"color": "#0000CC"}]]}

Exercice 2 : Somme de vecteurs à l'aide d'un quadrillage

Calculer la somme vectorielle suivante en utilisant la figure ci-dessus.
\(\overrightarrow{ED} - \overrightarrow{CD}\)
Vous utiliserez le symbole \(\overrightarrow{ }\) présent sur le clavier.

Exercice 3 : Décomposer un vecteur en utilisant la relation de Chasles pour passer par le point donné

Décomposer le vecteur \( \overrightarrow{ WC } \) en utilisant la relation de Chasles pour passer par le point \( N \).
On écrira la décomposition sous la forme \( \overrightarrow{ WC } \) = ...

Exercice 4 : Exprimer un vecteur en fonction de deux autres vecteurs - position aléatoire

Exprimer le vecteur \( \overrightarrow{w} \) en fonction des vecteurs \( \overrightarrow{u} \) et \( \overrightarrow{v} \).

{"init": {"range": [[-1.0, 11.0], [-1.0, 11.0]], "scale": [20, 20]}, "line": [[[0.0, 0.0], [10.0, 0.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 1.0], [10.0, 1.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 2.0], [10.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 3.0], [10.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 4.0], [10.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 5.0], [10.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 6.0], [10.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 7.0], [10.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 8.0], [10.0, 8.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 9.0], [10.0, 9.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 10.0], [10.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, 0.0], [0.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, 0.0], [1.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, 0.0], [2.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, 0.0], [3.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, 0.0], [4.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[5.0, 0.0], [5.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, 0.0], [6.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[7.0, 0.0], [7.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[8.0, 0.0], [8.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[9.0, 0.0], [9.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[10.0, 0.0], [10.0, 10.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, 2.0], [4.0, 6.0], {"subtype": "vector", "arrow-end": "classic-wide-long", "stroke": "#0080FF"}], [[4.0, 2.0], [2.0, 2.0], {"subtype": "vector", "arrow-end": "classic-wide-long", "stroke": "#FF0000"}], [[4.0, 2.0], [6.0, 7.0], {"subtype": "vector", "arrow-end": "classic-wide-long", "stroke": "#0000CC"}]], "label": [[[6.5, 6.0], "\\overrightarrow{u}", "center", {"color": "#0080FF"}], [[5.5, 2.0], "\\overrightarrow{v}", "center", {"color": "#FF0000"}], [[8.5, 6.0], "\\overrightarrow{w}", "center", {"color": "#0000CC"}]]}

Exercice 5 : Identifier la somme de deux vecteurs dans une figure

Compléter les sommes vectorielles suivantes en utilisant la figure :

\(\overrightarrow{GD} + \overrightarrow{JC}\) = .....
On donnera uniquement un vecteur en réponse. On utilisera le symbole \(\overrightarrow{ }\) présent sur le clavier virtuel.

\(\overrightarrow{LG} + \overrightarrow{DA}\) = .....
On donnera uniquement un vecteur en réponse. On utilisera le symbole \(\overrightarrow{ }\) présent sur le clavier virtuel.

\(\overrightarrow{MK} + \overrightarrow{DK}\) = .....
On donnera uniquement un vecteur en réponse. On utilisera le symbole \(\overrightarrow{ }\) présent sur le clavier virtuel.

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