Hướng dẫn giải Bài 10 (Trang 81 SGK Toán Hình học 12)

Giải bài toán sau đây bằng phương pháp tọa độ: Cho hình lập phương <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>B</mi><mi>C</mi><mi>D</mi><mo>.</mo><mi>A</mi><mo>'</mo><mi>B</mi><mo>'</mo><mi>C</mi><mo>'</mo><mi>D</mi><mo>'</mo></math> cạnh bằng 1. a) Chứng minh rằng hai mặt phẳng (AB'D') và (BC'D) song song với nhau. b) Tính khoảng cách giữa hai mặt phẳng nói trên. Giải: Chọn hệ trục tọa độ như hình vẽ. Ta có: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>(</mo><mn>0</mn><mo>;</mo><mn>0</mn><mo>;</mo><mn>0</mn><mo>)</mo><mo>,</mo><mo> </mo><mo> </mo><mo> </mo><mi>B</mi><mo>(</mo><mn>1</mn><mo>;</mo><mn>0</mn><mo>;</mo><mn>0</mn><mo>)</mo><mo>,</mo><mo> </mo><mo> </mo><mi>C</mi><mo>(</mo><mn>1</mn><mo>;</mo><mn>1</mn><mo>;</mo><mn>0</mn><mo>)</mo><mo>,</mo><mo> </mo><mo> </mo><mi>D</mi><mo>(</mo><mn>0</mn><mo>;</mo><mn>1</mn><mo>;</mo><mn>0</mn><mo>)</mo><mspace linebreak="newline"/><mi>A</mi><mo>'</mo><mo>(</mo><mn>0</mn><mo>;</mo><mn>0</mn><mo>;</mo><mn>1</mn><mo>)</mo><mo>,</mo><mo> </mo><mo> </mo><mi>B</mi><mo>'</mo><mo>(</mo><mn>1</mn><mo>;</mo><mn>0</mn><mo>;</mo><mn>1</mn><mo>)</mo><mo>,</mo><mo> </mo><mo> </mo><mi>C</mi><mo>'</mo><mo>(</mo><mn>1</mn><mo>;</mo><mn>1</mn><mo>;</mo><mn>1</mn><mo>)</mo><mo>,</mo><mo> </mo><mo> </mo><mi>D</mi><mo>'</mo><mo>(</mo><mn>0</mn><mo>;</mo><mn>1</mn><mo>;</mo><mn>1</mn><mo>)</mo><mspace linebreak="newline"/></math>   <img 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" width="350" height="195" /> a) Đặt <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>α</mi></mfenced><mo>=</mo><mo>(</mo><mi>A</mi><mi>B</mi><mo>'</mo><mi>D</mi><mo>'</mo><mo>)</mo><mo> </mo><mi>v</mi><mi>à</mi><mo> </mo><mfenced><mi>β</mi></mfenced><mo>=</mo><mo>(</mo><mi>B</mi><mi>C</mi><mo>'</mo><mi>D</mi><mo>)</mo><mo>.</mo></math> Ta có <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>A</mi><mi>B</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>=</mo><mo>(</mo><mn>1</mn><mo>;</mo><mn>0</mn><mo>;</mo><mn>1</mn><mo>)</mo><mo> </mo><mi>và</mi><mo> </mo><mover><mrow><mi>A</mi><mi>D</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>=</mo><mo>(</mo><mn>0</mn><mo>;</mo><mn>1</mn><mo>;</mo><mn>1</mn><mo>)</mo><mo>,</mo></math> suy ra mặt phẳng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>α</mi></mfenced></math> có vec tơ pháp tuyến là: <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><msub><mi>n</mi><mi>α</mi></msub><mo>→</mo></mover><mo>=</mo><mfenced open="[" close="]"><mrow><mover><mrow><mi>A</mi><mi>B</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>,</mo><mover><mrow><mi>A</mi><mi>D</mi><mo>'</mo></mrow><mo>→</mo></mover></mrow></mfenced><mo>=</mo><mo>(</mo><mn>1</mn><mo>;</mo><mn>1</mn><mo>-</mo><mn>1</mn><mo>)</mo></math> Vậy phương trình của mặt phẳng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>α</mi></mfenced></math> là x+y-z=0. Ta có <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>B</mi><mi>C</mi></mrow><mo>→</mo></mover><mo>'</mo><mo>=</mo><mo>(</mo><mn>0</mn><mo>;</mo><mn>1</mn><mo>;</mo><mn>1</mn><mo>)</mo></math> và <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>B</mi><mi>D</mi></mrow><mo>→</mo></mover><mo>=</mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>;</mo><mn>1</mn><mo>;</mo><mn>0</mn><mo>)</mo></math> Suy ra mặt phẳng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>β</mi></mfenced></math> có vec tơ pháp tuyến là <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><msub><mi>n</mi><mi>β</mi></msub><mo>→</mo></mover><mo>=</mo><mfenced open="[" close="]"><mrow><mover><mrow><mi>B</mi><mi>C</mi></mrow><mo>→</mo></mover><mo>'</mo><mo>,</mo><mover><mrow><mi>B</mi><mi>D</mi></mrow><mo>→</mo></mover></mrow></mfenced><mo>=</mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>;</mo><mo>-</mo><mn>1</mn><mo>;</mo><mn>1</mn><mo>)</mo></math> Phương trình mặt phẳng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>β</mi></mfenced></math> là: <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>(</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>-</mo><mn>1</mn><mo>.</mo><mi>y</mi><mo>+</mo><mn>1</mn><mo>.</mo><mi>z</mi><mo>=</mo><mn>0</mn><mo>⇔</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>-</mo><mi>z</mi><mo>-</mo><mn>1</mn><mo>=</mo><mn>0</mn><mo>.</mo></math> Ta có: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>1</mn></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>1</mn></mfrac><mo>=</mo><mfrac><mrow><mo>-</mo><mn>1</mn></mrow><mrow><mo>-</mo><mn>1</mn></mrow></mfrac><mo> </mo><mo>≠</mo><mfrac><mn>0</mn><mrow><mo>-</mo><mn>1</mn></mrow></mfrac></math>, vậy hai mặt phẳng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>α</mi></mfenced><mo> </mo><mi>và</mi><mo> </mo><mfenced><mi>β</mi></mfenced></math> song song với nhau. b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mfenced><mrow><mfenced><mi>α</mi></mfenced><mo>,</mo><mfenced><mi>β</mi></mfenced></mrow></mfenced><mo>=</mo><mi>d</mi><mfenced><mrow><mi>A</mi><mo>,</mo><mfenced><mi>β</mi></mfenced></mrow></mfenced><mo>=</mo><mfrac><mfenced open="|" close="|"><mrow><mo>-</mo><mn>1</mn></mrow></mfenced><msqrt><msup><mn>1</mn><mn>2</mn></msup><mo>+</mo><msup><mn>1</mn><mn>2</mn></msup><mo>+</mo><msup><mrow><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></mrow><mn>2</mn></msup></msqrt></mfrac><mo>=</mo><mfrac><mn>1</mn><msqrt><mn>3</mn></msqrt></mfrac><mo>.</mo></math>

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