Hướng dẫn giải Bài 2 (Trang 91 SGK Toán Hình học 11)

Cho hình hộp ABCD.A'B'C'D'. Chứng minh rằng:  <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>B</mi><mo>'</mo><mi>C</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>D</mi><mi>D</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>=</mo><mover><mrow><mi>A</mi><mi>C</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>;</mo><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mover><mrow><mi>B</mi><mi>D</mi></mrow><mo>→</mo></mover><mo>-</mo><mover><mrow><mi>D</mi><mo>'</mo><mi>D</mi></mrow><mo>→</mo></mover><mo>-</mo><mover><mrow><mi>B</mi><mo>'</mo><mi>D</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>=</mo><mover><mrow><mi>B</mi><mi>B</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>;</mo><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><mover><mrow><mi>A</mi><mi>C</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>B</mi><mi>A</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>D</mi><mi>B</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>C</mi><mo>'</mo><mi>D</mi></mrow><mo>→</mo></mover><mo>=</mo><mover><mn>0</mn><mo>→</mo></mover></math> Giải: a) Áp dụng quy tắc hình hộp ta có: <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>B</mi><mo>'</mo><mi>C</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>D</mi><mi>D</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>=</mo><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>A</mi><mi>D</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>A</mi><mi>A</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>=</mo><mover><mrow><mi>A</mi><mi>C</mi><mo>'</mo></mrow><mo>→</mo></mover></math> Cách khác <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>B</mi><mo>'</mo><mi>C</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>D</mi><mi>D</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>=</mo><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>B</mi><mi>C</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>C</mi><mi>C</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>=</mo><mover><mrow><mi>A</mi><mi>C</mi><mo>'</mo></mrow><mo>→</mo></mover></math> <img class="wscnph" src="https://static.colearn.vn:8413/v1.0/upload/library/24022022/93322b5e-7a43-421e-a4f2-d3472ade2aff.PNG" /> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">b</mi><mo>)</mo><mo> </mo><mover><mrow><mi>B</mi><mi>D</mi></mrow><mo>→</mo></mover><mo>-</mo><mover><mrow><mi>D</mi><mi>D</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>-</mo><mover><mrow><mi>B</mi><mi>D</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>=</mo><mover><mrow><mi>B</mi><mi>D</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>D</mi><mi>D</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>D</mi><mo>'</mo><mi>B</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>=</mo><mover><mrow><mi>B</mi><mi>B</mi><mo>'</mo></mrow><mo>→</mo></mover><mspace linebreak="newline"/><mi mathvariant="normal">c</mi><mo>)</mo><mo> </mo><mover><mrow><mi>A</mi><mi>C</mi><mo> </mo></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>B</mi><mi>A</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>D</mi><mi>B</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>C</mi><mo>'</mo><mi>D</mi></mrow><mo>→</mo></mover><mo>=</mo><mover><mrow><mi>A</mi><mi>C</mi></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>C</mi><mi>D</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>D</mi><mo>'</mo><mi>B</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>B</mi><mo>'</mo><mi>A</mi></mrow><mo>→</mo></mover><mo>=</mo><mover><mrow><mi>A</mi><mi>A</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>=</mo><mover><mn>0</mn><mo>→</mo></mover></math>

Giải bài tập 2 (SGK Toán 11, trang 91, Hình học)

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