Bài 2 trang 91 sgk hình học 11: Bài 1. Vectơ trong không gian...
Bài 2 trang 91 sgk hình học 11: Bài 1. Vectơ trong không gian. Cho hình hộp ABCD.A'B'C'D'. Chứng minh rằng: Bài 2 . Cho hình hộp (ABCD.A’B’C’D’). Chứng minh rằng: a) (overrightarrow{AB}) + (overrightarrow{B’C’}) + (overrightarrow{DD’}) = ...
Bài 2. Cho hình hộp (ABCD.A’B’C’D’). Chứng minh rằng:
a) (overrightarrow{AB}) + (overrightarrow{B’C’}) + (overrightarrow{DD’}) = (overrightarrow{AC’});
b) (overrightarrow{BD}) – (overrightarrow{D’D}) – (overrightarrow{B’D’}) = (overrightarrow{BB’});
c) (overrightarrow{AC}) + (overrightarrow{BA’}) + (overrightarrow{DB}) + (overrightarrow{C’D}) = (overrightarrow{0}).
Giải
a) (overrightarrow{AB}) + (overrightarrow{B’C’}) + (overrightarrow{DD’}) = (overrightarrow{AB}) + (overrightarrow{BC}) + (overrightarrow{CC’}) = (overrightarrow{AC’});
b) (overrightarrow{BD}) – (overrightarrow{D’D}) – (overrightarrow{B’D’}) = (overrightarrow{BD}) + (overrightarrow{DD’}) + (overrightarrow{D’B’}) = (overrightarrow{BB’});
c) (overrightarrow{AC}) + (overrightarrow{BA’}) + (overrightarrow{DB}) + (overrightarrow{C’D}) = (overrightarrow{AC}) + (overrightarrow{CD’}) + (overrightarrow{D’B’}) + (overrightarrow{B’A}) = (overrightarrow{0}).