Hướng dẫn giải Câu 14 (Trang 97 SGK Toán Hình học 12)

Cho mặt phẳng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>α</mi></mfenced></math>: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mn>3</mn><mi>z</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0</mn></math> và đường thẳng d có phương trình tham số: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>3</mn><mo>+</mo><mi>t</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mn>2</mn><mo>-</mo><mn>2</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></math> Trong các mệnh đề sau, mệnh đề nào đúng? <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>A</mi></mfenced><mo> </mo><mi>d</mi><mo>⊥</mo><mfenced><mi>α</mi></mfenced><mo>;</mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mi>B</mi></mfenced><mo> </mo><mi>d</mi><mo> </mo><mi>c</mi><mi>ắ</mi><mi>t</mi><mo> </mo><mfenced><mi>α</mi></mfenced><mo>;</mo><mspace linebreak="newline"/><mo>(</mo><mi>C</mi><mo>)</mo><mo> </mo><mi>d</mi><mo>/</mo><mo>/</mo><mo> </mo><mfenced><mi>α</mi></mfenced><mo>;</mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mi>D</mi></mfenced><mo> </mo><mi>d</mi><mo> </mo><mo>⊂</mo><mo> </mo><mfenced><mi>α</mi></mfenced><mo>.</mo></math> Giải Vec tơ pháp tuyết của <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>α</mi></mfenced></math> là <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>n</mi><mo>→</mo></mover></math> = (2; 1; 3) Vec tơ chỉ phương của d là <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>a</mi><mo>→</mo></mover></math> = (1; -2 ; 0) Ta có <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>n</mi><mo>→</mo></mover><mo>.</mo><mover><mi>a</mi><mo>→</mo></mover><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn><mo>-</mo><mn>2</mn><mo>=</mo><mn>0</mn></math> d đi qua <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>M</mi><mn>0</mn></msub><mo>(</mo><mo>-</mo><mn>3</mn><mo>;</mo><mo> </mo><mn>2</mn><mo>;</mo><mo> </mo><mn>1</mn><mo>)</mo><mo> </mo><mo>∈</mo><mo> </mo><mfenced><mi>α</mi></mfenced><mo> </mo><mi>n</mi><mi>ê</mi><mi>n</mi><mo> </mo><mi>d</mi><mo>⊂</mo><mfenced><mi>α</mi></mfenced><mo>.</mo><mo> </mo><mi>c</mi><mi>h</mi><mi>ọ</mi><mi>n</mi><mo> </mo><mo>(</mo><mi>D</mi><mo>)</mo><mo>.</mo></math>