Hướng dẫn giải Câu 12 (Trang 96 SGK Toán Hình học 12)

cho d là đường thẳng đi qua điểm A (1; 2; 3) và vuông góc với 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>4</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>y</mi><mo>-</mo><mn>7</mn><mi>z</mi><mo>+</mo><mn>1</mn><mo>=</mo><mn>0</mn></math>. Phương trình tham số của d là: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>A</mi></mfenced><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>+</mo><mn>4</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>+</mo><mn>3</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mn>3</mn><mo>-</mo><mn>7</mn><mi>t</mi></mtd></mtr></mtable></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><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mi>B</mi></mfenced><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mn>1</mn><mo>+</mo><mn>4</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mn>2</mn><mo>+</mo><mn>3</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mn>3</mn><mo>-</mo><mn>7</mn><mi>t</mi></mtd></mtr></mtable></mfenced><mo>;</mo><mspace linebreak="newline"/><mfenced><mi>C</mi></mfenced><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mn>1</mn><mo>+</mo><mn>3</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mn>2</mn><mo>-</mo><mn>4</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mn>3</mn><mo>-</mo><mn>7</mn><mi>t</mi></mtd></mtr></mtable></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><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mfenced><mi>D</mi></mfenced><mo> </mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>+</mo><mn>8</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mn>2</mn><mo>+</mo><mn>6</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>-</mo><mn>3</mn><mo>-</mo><mn>14</mn><mi>t</mi></mtd></mtr></mtable></mfenced><mo>.</mo></math> Giải Vectơ 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><mo>=</mo><mo>(</mo><mn>4</mn><mo>;</mo><mo> </mo><mn>3</mn><mo>;</mo><mo> </mo><mo>-</mo><mn>7</mn><mo>)</mo></math>, d vuông góc với <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>α</mi></mfenced></math> thì d có vectơ chỉ phương <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><msub><mi>a</mi><mi>d</mi></msub><mo>→</mo></mover><mo>=</mo><mover><mi>n</mi><mo>→</mo></mover><mo>=</mo><mo>(</mo><mn>4</mn><mo>;</mo><mo> </mo><mn>3</mn><mo>;</mo><mo> </mo><mo>-</mo><mn>7</mn><mo>)</mo></math> Phương trình tham số của d là: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mn>1</mn><mo>+</mo><mn>4</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mn>2</mn><mo>+</mo><mn>3</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mn>3</mn><mo>-</mo><mn>7</mn><mi>t</mi></mtd></mtr></mtable></mfenced></math>. Chọn (B).