Hướng dẫn giải Bài 8 (Trang 92 SGK Toán Hình học 11)

Cho hình lăng trụ tam giác ABC.A'B'C' có <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>A</mi><mi>A</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>=</mo><mover><mi>a</mi><mo>→</mo></mover><mo>,</mo><mo> </mo><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>→</mo></mover><mo>=</mo><mover><mi>b</mi><mo>→</mo></mover><mo>,</mo><mover><mrow><mi>A</mi><mi>C</mi></mrow><mo>→</mo></mover><mo>=</mo><mover><mi>c</mi><mo>→</mo></mover></math>. Hãy phân tích (hay biểu thị) các vecto  <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>B</mi><mo>'</mo><mi>C</mi></mrow><mo>→</mo></mover><mo>,</mo><mo> </mo><mover><mrow><mi>B</mi><mi>C</mi><mo>'</mo></mrow><mo>→</mo></mover></math> qua các vecto <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>a</mi><mo>→</mo></mover><mo>,</mo><mo> </mo><mover><mi>b</mi><mo>→</mo></mover><mo>,</mo><mo> </mo><mover><mi>c</mi><mo>→</mo></mover></math>. Giải: <img class="wscnph" src="https://static.colearn.vn:8413/v1.0/upload/library/24022022/042a8084-02a0-4332-83d6-f1b227b7b91c.PNG" /> Ta có: <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mrow><mi>B</mi><mo>'</mo><mi>C</mi></mrow><mo>→</mo></mover><mo>=</mo><mover><mrow><mi>A</mi><mi>C</mi></mrow><mo>→</mo></mover><mo>-</mo><mover><mrow><mi>A</mi><mi>B</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>=</mo><mover><mrow><mi>A</mi><mi>C</mi></mrow><mo>→</mo></mover><mo>-</mo><mfenced><mrow><mover><mrow><mi>A</mi><mi>A</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>→</mo></mover></mrow></mfenced><mspace linebreak="newline"/><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><mover><mi>c</mi><mo>→</mo></mover><mo>-</mo><mover><mi>a</mi><mo>→</mo></mover><mo>-</mo><mover><mi>b</mi><mo>→</mo></mover><mspace linebreak="newline"/><mover><mrow><mi>B</mi><mo>'</mo><mi>C</mi></mrow><mo>→</mo></mover><mo>=</mo><mover><mrow><mi>A</mi><mi>C</mi></mrow><mo>→</mo></mover><mo>-</mo><mover><mrow><mi>A</mi><mi>B</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>=</mo><mfenced><mrow><mover><mrow><mi>A</mi><mi>A</mi><mo>'</mo></mrow><mo>→</mo></mover><mo>+</mo><mover><mrow><mi>A</mi><mi>C</mi></mrow><mo>→</mo></mover></mrow></mfenced><mo>-</mo><mover><mrow><mi>A</mi><mi>B</mi></mrow><mo>→</mo></mover><mspace linebreak="newline"/><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><mover><mi>a</mi><mo>→</mo></mover><mo>+</mo><mover><mi>c</mi><mo>→</mo></mover><mo>-</mo><mover><mi>b</mi><mo>→</mo></mover><mspace linebreak="newline"/></math>

Giải bài tập 8 (SGK Toán 11, trang 92, Hình học)

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