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Bài 8.27 trang 79 SGK Toán 11 tập 2 - Cùng khám phá

Cho hình hộp chữ nhật ABCD.A’B’C’D’ có AB = a, BC = b.
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Đề bài

Cho hình hộp chữ nhật ABCD.A’B’C’D’ có AB = a, BC = b. Tính khoảng cách giữa hai đường thẳng BB’ và AC’.

Phương pháp giải - Xem chi tiết

Chọn (P) chứa a và song song với b. Khi đó khoảng cách a và b là khoảng cách giữa b và (P).

Lời giải chi tiết

Ta có: CC’ // BB’ nên BB’ // (ACC’A’)Suy ra khoảng cách giữa BB’ và AC’ là khoảng cách giữa BB’ và (ACC’A’) hay khoảng cách giữa B là (ACC’A’)Kẻ BH vuông góc với AC\(\begin{array}{l}AC = \sqrt {{a^2} + {b^2}} \\AB.BC = BH.AC\\ \Leftrightarrow BH = \frac{{ab}}{{\sqrt {{a^2} + {b^2}} }}\end{array}\)

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