Hướng dẫn giải Hoạt động 6 (Trang 89 SGK Toán Hình học 11)

Đề bài Cho hai vecto <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>a</mi><mo>→</mo></mover></math>; <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>b</mi><mo>→</mo></mover></math> đều khác vecto <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mn>0</mn><mo>→</mo></mover></math>. Hãy xác định vecto <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>c</mi><mo>→</mo></mover></math>=<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>a</mi><mo>→</mo></mover></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>b</mi><mo>→</mo></mover></math> và giải thích tại sao ba vecto <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>a</mi><mo>→</mo></mover></math>; <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>b</mi><mo>→</mo></mover></math>; <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>c</mi><mo>→</mo></mover></math> đồng phẳng. Phương pháp giải  <div class="content_method_content"> - Dựng hai véc tơ <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>a</mi><mo>→</mo></mover></math>; <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>b</mi><mo>→</mo></mover></math> - Chọn một điểm làm gốc, vẽ hai véc tơ <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>a</mi><mo>→</mo></mover></math>; <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>b</mi><mo>→</mo></mover></math> - Sử dụng quy tắc hình bình hành dựng véc tơ <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>c</mi><mo>→</mo></mover></math> </div> Lời giải chi tiết <img src="https://img.loigiaihay.com/picture/2021/1227/110.PNG" width="570" height="190" /> <span id="MathJax-Element-8-Frame" class="mjx-chtml MathJax_CHTML" style="margin: 0px; padding: 1px 0px; display: inline-block; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 21.78px; letter-spacing: normal; overflow-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; position: relative;" tabindex="0" role="presentation" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>a</mi><mo>&#x2192;</mo></mover><mo>;</mo><mspace width="thinmathspace" /><mover><mi>b</mi><mo>&#x2192;</mo></mover><mo>;</mo><mspace width="thinmathspace" /><mover><mi>c</mi><mo>&#x2192;</mo></mover></math>"> <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>a</mi><mo>→</mo></mover></math>; <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>b</mi><mo>→</mo></mover></math>; <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>c</mi><mo>→</mo></mover></math> đồng phẳng vì <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>a</mi><mo>→</mo></mover></math>; <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>b</mi><mo>→</mo></mover></math>  không cùng phương và có cặp số (2; -1) sao cho : <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>c</mi><mo>→</mo></mover></math>= <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>a</mi><mo>→</mo></mover></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>b</mi><mo>→</mo></mover></math>

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