Hướng dẫn giải Bài 1 (Trang 68 SGK Toán Hình học 12)

Cho ba vecto <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>a</mi><mo>→</mo></mover><mo>=</mo><mo>(</mo><mn>2</mn><mo>;</mo><mo>-</mo><mn>5</mn><mo>;</mo><mn>3</mn><mo>)</mo><mo>,</mo><mo> </mo><mover><mi>b</mi><mo>→</mo></mover><mo>=</mo><mo>(</mo><mn>0</mn><mo>;</mo><mn>2</mn><mo>;</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>,</mo><mover><mi>c</mi><mo>→</mo></mover><mo>=</mo><mo>(</mo><mn>1</mn><mo>;</mo><mn>7</mn><mo>;</mo><mn>2</mn><mo>)</mo></math> a) Tính tọa độ của vecto <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>d</mi><mo>→</mo></mover><mo>=</mo><mn>4</mn><mover><mi>a</mi><mo>→</mo></mover><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mover><mi>b</mi><mo>→</mo></mover><mo>+</mo><mn>3</mn><mover><mi>c</mi><mo>→</mo></mover></math> b) Tính tọa độ của vecto <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>e</mi><mo>→</mo></mover><mo>=</mo><mover><mi>a</mi><mo>→</mo></mover><mo>-</mo><mn>4</mn><mover><mi>b</mi><mo>→</mo></mover><mo>-</mo><mn>2</mn><mover><mi>c</mi><mo>→</mo></mover></math>. Giải a) Ta có: <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mover><mi>a</mi><mo>→</mo></mover><mo>=</mo><mo>(</mo><mn>8</mn><mo>;</mo><mo>-</mo><mn>20</mn><mo>;</mo><mn>12</mn><mo>)</mo><mo>;</mo><mo> </mo><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mover><mi>b</mi><mo>→</mo></mover><mo>=</mo><mfenced><mrow><mn>0</mn><mo>;</mo><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>;</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow></mfenced><mspace linebreak="newline"/><mn>3</mn><mover><mi>c</mi><mo>→</mo></mover><mo>=</mo><mo>(</mo><mn>3</mn><mo>;</mo><mn>21</mn><mo>;</mo><mn>6</mn><mo>)</mo></math> Do đó: <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>d</mi><mo>→</mo></mover><mo>=</mo><mn>4</mn><mover><mi>a</mi><mo>→</mo></mover><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mover><mi>b</mi><mo>→</mo></mover><mo>+</mo><mn>3</mn><mo>=</mo><mfenced><mrow><mn>11</mn><mo>;</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>;</mo><mfrac><mn>55</mn><mn>3</mn></mfrac></mrow></mfenced></math> b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>e</mi><mo>→</mo></mover><mo>=</mo><mover><mi>a</mi><mo>→</mo></mover><mo>-</mo><mn>4</mn><mover><mi>b</mi><mo>→</mo></mover><mo>-</mo><mn>2</mn><mover><mi>c</mi><mo>→</mo></mover><mo>=</mo><mfenced><mrow><mn>0</mn><mo>;</mo><mo>-</mo><mn>27</mn><mo>;</mo><mn>3</mn></mrow></mfenced></math>