Hướng dẫn giải Bài 9 (Trang 81 SGK Toán Hình học 12)
<p>Tính khoảng cách từ điểm A(2;4;-3) lần lượt đến các mặt phẳng sau:</p>
<p>a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mn>2</mn><mi>z</mi><mo>-</mo><mn>9</mn><mo>=</mo><mn>0</mn><mo>;</mo></math></p>
<p>b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mi>x</mi><mo>-</mo><mn>5</mn><mi>z</mi><mo>+</mo><mn>5</mn><mo>=</mo><mn>0</mn><mo>;</mo></math></p>
<p>c) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mn>0</mn><mo>.</mo></math></p>
<p><strong>Giải:</strong></p>
<p>a) Với mặt phẳng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>α</mi></mfenced><mo>:</mo><mo> </mo><mn>2</mn><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mn>2</mn><mi>z</mi><mo>-</mo><mn>9</mn><mo>=</mo><mn>0</mn></math></p>
<p><span class="mce-nbsp-wrap" contenteditable="false"> </span>Ta có: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>(</mo><mi>A</mi><mo>,</mo><mfenced><mi>α</mi></mfenced><mo>)</mo><mo>=</mo><mfrac><mfenced open="|" close="|"><mrow><mn>2</mn><mo>.</mo><mn>2</mn><mo>-</mo><mn>4</mn><mo>+</mo><mn>2</mn><mo>(</mo><mo>-</mo><mn>3</mn><mo>)</mo><mo>-</mo><mn>9</mn></mrow></mfenced><msqrt><mn>4</mn><mo>+</mo><mn>1</mn><mo>+</mo><mn>4</mn></msqrt></mfrac><mo>=</mo><mn>5</mn></math></p>
<p>b) Với mặt phẳng <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>β</mi></mfenced><mo>:</mo><mo> </mo><mn>12</mn><mi>x</mi><mo>-</mo><mn>5</mn><mi>z</mi><mo>+</mo><mn>5</mn><mo>=</mo><mn>0</mn></math></p>
<p><span class="mce-nbsp-wrap" contenteditable="false"> </span>Ta có: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>(</mo><mi>A</mi><mo>,</mo><mfenced><mi>β</mi></mfenced><mo>)</mo><mo>=</mo><mfrac><mfenced open="|" close="|"><mrow><mn>12</mn><mo>(</mo><mn>2</mn><mo>)</mo><mo>-</mo><mn>5</mn><mo>(</mo><mo>-</mo><mn>3</mn><mo>)</mo><mo>+</mo><mn>5</mn></mrow></mfenced><msqrt><mn>144</mn><mo>+</mo><mn>25</mn></msqrt></mfrac><mo>=</mo><mfrac><mn>44</mn><mn>13</mn></mfrac></math></p>
<p>c) Với mặt phẳng<math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi>γ</mi></mfenced><mo>:</mo><mi>x</mi><mo>=</mo><mn>0</mn><mo>,</mo><mo> </mo><mi>ta</mi><mo> </mo><mi>có</mi><mo> </mo><mo> </mo><mi>d</mi><mfenced><mrow><mi>A</mi><mo>,</mo><mfenced><mi>γ</mi></mfenced></mrow></mfenced><mo>=</mo><mfrac><mfenced open="|" close="|"><mn>2</mn></mfenced><msqrt><mn>1</mn><mo>+</mo><mn>0</mn><mo>+</mo><mn>0</mn></msqrt></mfrac><mo>=</mo><mn>2</mn><mo>.</mo></math></p>