Hướng dẫn giải Câu 11 (Trang 96 SGK Toán Hình học 12)

Cho đường thẳng <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo></math> đi qua điểm M (2; 0; -1) và có vectơ chỉ phương <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>α</mi><mo>→</mo></mover><mo>=</mo><mo>(</mo><mn>4</mn><mo>;</mo><mo> </mo><mo>-</mo><mn>6</mn><mo>;</mo><mo> </mo><mn>2</mn><mo>)</mo></math>. Phương trình tham số của đường thẳng <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo></math> là: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>A</mi></mfenced><mo> </mo><mfenced open="{" close=""><mrow><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>+</mo><mn>4</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mo>-</mo><mn>6</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mn>1</mn><mo>+</mo><mn>2</mn><mi>t</mi></mtd></mtr></mtable><mo>;</mo></mrow></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><mfenced><mi>B</mi></mfenced><mo> </mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>+</mo><mn>2</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mo>-</mo><mn>3</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mn>1</mn><mi>_</mi><mi>t</mi></mtd></mtr></mtable></mfenced><mo>;</mo><mspace linebreak="newline"/><mspace linebreak="newline"/><mfenced><mi>C</mi></mfenced><mo> </mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mn>2</mn><mo>+</mo><mn>2</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mo>-</mo><mn>3</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>+</mo><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><mfenced><mi>D</mi></mfenced><mo> </mo><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mn>4</mn><mo>+</mo><mn>2</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mo>-</mo><mn>6</mn><mo>-</mo><mn>3</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mn>2</mn><mo>+</mo><mi>t</mi></mtd></mtr></mtable></mfenced><mo>.</mo></math> Giải Ta có <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>a</mi><mo> </mo></mrow><mo>→</mo></mover><mo>=</mo><mn>2</mn><mover><mi>a</mi><mo>→</mo></mover><mo> </mo><mi>v</mi><mi>ớ</mi><mi>i</mi><mo> </mo><mover><mi>a</mi><mo>→</mo></mover><mo>=</mo><mo>(</mo><mn>2</mn><mo>;</mo><mo> </mo><mo>-</mo><mn>3</mn><mo>;</mo><mo> </mo><mn>1</mn><mo>)</mo></math> Phương trình tham số của <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo></math> là <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced open="{" close=""><mtable columnalign="left"><mtr><mtd><mi>x</mi><mo>=</mo><mn>2</mn><mo>+</mo><mn>2</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mo>-</mo><mn>3</mn><mi>t</mi></mtd></mtr><mtr><mtd><mi>z</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>+</mo><mi>t</mi></mtd></mtr></mtable></mfenced></math>. Chọn (D)