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Giải bài 5 trang 65 sách bài tập toán 12 - Chân trời sáng tạo

Trong không gian (Oxyz) (đơn vị trên các trục toạ độ là centimét), đầu in phun của một máy in 3D đang đặt tại điểm (Mleft( {5;0;35} right)). Tính khoảng cách từ đầu in phun đến khay đặt vật in có phương trình (z - 5 = 0).

🎃Tổng hợp đề thi học kì 2 lớp 12 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Hoá - Sinh - Sử - Địa
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Đề bài

Trong không gian \(Oxyz\) (đơn vị trên các trục toạ độ là centimét), đầu in phun của một máy in 3D đang đặt tại điểm \(M\left( {5;0;35} \right)\). Tính khoảng cách từ đầu in phun đến khay đặt vật in có phương trình \(z - 5 = 0\).

Phương pháp giải - Xem chi tiết

Khoảng cách từ điểm \({M_0}\left( {{x_0};{y_0};{z_0}} \right)\) đến mặt phẳng \(\left( P \right):Ax + By + C{\rm{z}} + D = 0\): \(d\left( {{M_0};\left( P \right)} \right) = \frac{{\left| {A{x_0} + B{y_0} + C{{\rm{z}}_0} + D} \right|}}{{\sqrt {{A^2} + {B^2} + {C^2}} }}\).

Lời giải chi tiết

Khoảng cách từ đầu in phun đến khay đặt vật in là: \(d\left( {M;\left( P \right)} \right) = \frac{{\left| {35 - 5} \right|}}{{\sqrt {{0^2} + {0^2} + {1^2}} }} = 30\left( {cm} \right)\).

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