On représente ci dessous deux vecteurs \(\overrightarrow{AB}\) et \(\overrightarrow{CD}\) dans le plan.
{"init": {"range": [[-8.0, 11.0], [-8.0, 8.0]], "scale": [20, 20]}, "line": [[[-7.0, -7.0], [10.0, -7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -6.0], [10.0, -6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -5.0], [10.0, -5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -4.0], [10.0, -4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -3.0], [10.0, -3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -2.0], [10.0, -2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -1.0], [10.0, -1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, 0.0], [10.0, 0.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, 1.0], [10.0, 1.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, 2.0], [10.0, 2.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, 3.0], [10.0, 3.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, 4.0], [10.0, 4.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, 5.0], [10.0, 5.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, 6.0], [10.0, 6.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, 7.0], [10.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-7.0, -7.0], [-7.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, -7.0], [-6.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-5.0, -7.0], [-5.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-4.0, -7.0], [-4.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-3.0, -7.0], [-3.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-2.0, -7.0], [-2.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-1.0, -7.0], [-1.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[0.0, -7.0], [0.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[1.0, -7.0], [1.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[2.0, -7.0], [2.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[3.0, -7.0], [3.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[4.0, -7.0], [4.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[5.0, -7.0], [5.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[6.0, -7.0], [6.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[7.0, -7.0], [7.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[8.0, -7.0], [8.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[9.0, -7.0], [9.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[10.0, -7.0], [10.0, 7.0], {"subtype": "segment", "stroke": "#ccc"}], [[-6.0, 5.0], [-2.0, 0.0], {"subtype": "vector", "arrow-end": "classic-wide-long", "stroke": "#3371FF"}], [[1.0, 4.0], [9.0, -6.0], {"subtype": "vector", "arrow-end": "classic-wide-long", "stroke": "#E11916"}]], "label": [[[-6.0, 5.0], "A", "above", {}], [[-2.0, 0.0], "B", "above", {}], [[1.0, 4.0], "C", "above", {}], [[9.0, -6.0], "D", "above", {}]], "circle": [[[-6.0, 5.0], 0.1, {}], [[-2.0, 0.0], 0.1, {}], [[1.0, 4.0], 0.1, {}], [[9.0, -6.0], 0.1, {}]]}
Compléter la relation de colinéarité suivante :
\(\overrightarrow{CD}\) = ... \(\overrightarrow{AB}\)
On attendra une réponse sous la forme d'un nombre réel.