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Bài 8.39 trang 89 SGK Toán 11 tập 2 - Cùng khám phá

Cho hình lập phương ABCD.A’B’C’D’ cạnh a.
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Đề bài

Cho hình lập phương ABCD.A’B’C’D’ cạnh a. a) Chứng minh BC vuông góc với mặt phẳng (A’B’CD). b) Tính khoảng cách giữa hai đường thẳng AB’ và BC’.

Phương pháp giải - Xem chi tiết

Đường thẳng d vuông góc với 2 đường thẳng cắt nhau nằm trong (P) thì d vuông góc với (P).

Lời giải chi tiết

a) BC vuông góc với CD (ABCD là hình vuông)BC vuông với (ADD’A’) nên BC vuông góc với A’DSuy ra BC vuông góc với (A’B’CD)b) Gọi giao điểm của B’C và BC’ là F, A’D và AD’ là EKẻ FH vuông góc với BC’ nên FH vuông góc với AD’Kẻ HK // BC’, KI // HFVậy KI là đường vuông góc chung của AB’ và BC’.

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