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Giả sử mặt phẳng (P) có dạng:
$\begin{array}{l}
Ax + By + Cz + D = 0\,\,({A^2} + {B^2} + {C^2} \ne 0) \Rightarrow \overrightarrow {{n_P}} = (A;B;C).\\
(d)//(P) \Rightarrow {\rm A} + 2B + C = 0\, \Rightarrow C = - A - 2B\\
A \in (P) \Rightarrow - C + D = 0\, \Rightarrow D = - C\,\\
d(O,(P)) = \frac{3}{{\sqrt {14} }} \Leftrightarrow \frac{{|D|}}{{\sqrt {{A^2} + {B^2} + {C^2}} }} = \frac{3}{{\sqrt {14} }} \Rightarrow \left[ \begin{array}{l}
B = - 2A\\
B = \frac{{2A}}{{11}}
\end{array} \right.
\end{array}$
TH1: $B = - 2A$, chọn $A = 1,B = - 2 \Rightarrow C = 3,D = 3 $
$\Rightarrow (P):x - 2y + 3z + 3 = 0$
TH2: $B = \frac{{2A}}{{11}}$, chọn $A = 11,B = 2 \Rightarrow C = - 15,D = 15$
$ \Rightarrow (P):11x + 2y - 15z + 15 = 0$
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