Cùng Trường TCSP Mẫu giáo – Nhà trẻ Hà Nội tìm hiểu Viết phương trình đường thẳng qua A vuông góc với d1 cắt d2 trong Oxyz – Toán 12 chuyên đề
Vậy cách Viết phương trình đường thẳng qua A vuông góc với d1 cắt d2 trong Oxyz như thế nào? chúng ta sẽ cùng tìm hiểu qua bài viết dưới đây và cùng xem các bài tập và ví dụ minh họa để hiểu rõ nhé.
Các em có thể xem lại nội dung Lý thuyết và các dạng bài tập Phương trình đường thẳng trong Oxyz nếu các em chưa nhớ rõ phần kiến thức này.
° Viết phương trình đường thẳng qua A vuông góc với d1 cắt d2 trong Oxyz
– Cho trước tọa độ điểm A và phương trình 2 đường thẳng (d1), (d2). Hãy viết phương trình đường thẳng qua A vuông góc với d1 cắt d2 trong Oxyz.
* Phương pháp
+ Cách giải 1:
– Bước 1: Viết PT mặt phẳng (α) qua điểm A và vuông góc đường thẳng d1.
– Bước 2: Tìm giao điểm B = (α) ∩ (d2)
– Bước 3: Đường thẳng cần tìm là đường thẳng đi qua 2 điểm A, B.
+ Cách giải 2:
– Bước 1: Viết PT mp (α) đi qua điểm A và vuông góc với d1.
– Bước 2: Viết PT mp (β) đi qua điểm A và chứa d2.
– Bước 3: Đường thẳng cần tìm d = (α) ∩ (β)
* Ví dụ 1: Trong không gian với hệ toạ độ Oxyz, viết phương trình đường thẳng (d) đi qua M(1;1;1), cắt đường thẳng d1: 
và vuông góc với đường thẳng d2: x=-2+2t; y=-5t; z=2+t;
* Lời giải:
– Phương trình mp (P) ⊥ d2 nên nhận VTCP d2 làm VTPT nên có PT:
2x – 5y + z + D = 0
– Phương trình mp (P) đi qua M(1;1;1) nên có:
2.1 – 5.1 + 1 + D = 0 ⇒ D = 2
⇒ Phương trình mp (P):
2x – 5y + z + 2 = 0
– Toạ độ giao điểm A của d1 và mp(P) là: (-5;-1;3)
⇒ 
= (6;2;-2) = (3;1;-1)
⇒ PTTQ của (d) là: 
Hy vọng với bài viết về cách viết phương trình đường thẳng qua A vuông góc với d1 cắt d2 trong Oxyz ở trên hữu ích cho các em. Mọi thắc mắc các em vui lòng để lại bình luận dưới bài viết để Trường TCSP Mẫu giáo – Nhà trẻ Hà Nội ghi nhận và hỗ trợ. Chúc các em học tập tốt!
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