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Bài 4.7 trang 100 SGK Toán 11 tập 1 - Cùng khám phá

Cho tứ diện ABCD. Gọi M, N là hai điểm phân biệt cùng thuộc đường thẳng AD và P, Q là hai điểm phân biệt cùng thuộc đường thẳng BC. Xét vị trí tương đối của hai đường thẳng MQ, NP và vị trí tương đối của hai đường thẳng MP, NQ.
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Đề bài

Cho tứ diện ABCD. Gọi M, N là hai điểm phân biệt cùng thuộc đường thẳng AD và P, Q là hai điểm phân biệt cùng thuộc đường thẳng BC. Xét vị trí tương đối của hai đường thẳng MQ, NP và vị trí tương đối của hai đường thẳng MP, NQ.

Phương pháp giải - Xem chi tiết

Hai đường thẳng chéo nhau là hai đường thẳng không đồng phẳng.

Lời giải chi tiết

Giả sử MP và QN, MQ và PN cùng nằm trong một mặt phẳng. Suy ra M, P, Q, N thuộc cùng một mặt phẳng.Mà M, N thuộc AD; P, Q thuộc BC. Nên AD, BC cũng cùng thuộc một mặt phẳng.Tức là A, B, C, D đồng phẳng (Mâu thuẫn).Vậy MP và QN chéo nhau, MQ và PN chéo nhau.

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