Trong không gian với hệ tọa độ Oxyz, cho hai mặt phẳng\(({{P}_{1}})\): \({{A}_{1}}x+{{B}_{1}}y+{{C}_{1}}z+{{D}_{1}}=0\) và \(({{P}_{2}})\): \({{A}_{2}}x+{{B}_{2}}y+{{C}_{2}}z+{{D}_{2}}=0\). Chọn các khẳng định đúng
I. \(({{P}_{1}})\)cắt \(({{P}_{2}})\) \( \Leftrightarrow {A_1}:{B_1}:{C_1} \ne {A_2}:{B_2}:{C_2}\)
II. \(({P_1})//({P_2}) \Leftrightarrow \dfrac{{{A_1}}}{{{A_2}}} = \dfrac{{{B_1}}}{{{B_2}}} = \dfrac{{{C_1}}}{{{C_2}}}\)
III. \(({{P}_{1}})\)\(\equiv \) \(({{P}_{2}})\)\(\leftrightarrow \dfrac{{{A}_{1}}}{{{A}_{2}}}=\dfrac{{{B}_{1}}}{{{B}_{2}}}=\dfrac{{{C}_{1}}}{{{C}_{2}}}=\dfrac{{{D}_{1}}}{{{D}_{2}}}\)
IV. \({P_1})//({P_2}) \Leftrightarrow \dfrac{{{A_1}}}{{{A_2}}} = \dfrac{{{B_1}}}{{{B_2}}} = \dfrac{{{C_1}}}{{{C_2}}} \ne \dfrac{{{D_1}}}{{{D_2}}}\)
A.I,II,III
B.I,III,IV
C.II,III,IV
D.I,II,IV
I. \(({{P}_{1}})\)cắt \(({{P}_{2}})\) \( \Leftrightarrow {A_1}:{B_1}:{C_1} \ne {A_2}:{B_2}:{C_2}\)
II. \(({P_1})//({P_2}) \Leftrightarrow \dfrac{{{A_1}}}{{{A_2}}} = \dfrac{{{B_1}}}{{{B_2}}} = \dfrac{{{C_1}}}{{{C_2}}}\)
III. \(({{P}_{1}})\)\(\equiv \) \(({{P}_{2}})\)\(\leftrightarrow \dfrac{{{A}_{1}}}{{{A}_{2}}}=\dfrac{{{B}_{1}}}{{{B}_{2}}}=\dfrac{{{C}_{1}}}{{{C}_{2}}}=\dfrac{{{D}_{1}}}{{{D}_{2}}}\)
IV. \({P_1})//({P_2}) \Leftrightarrow \dfrac{{{A_1}}}{{{A_2}}} = \dfrac{{{B_1}}}{{{B_2}}} = \dfrac{{{C_1}}}{{{C_2}}} \ne \dfrac{{{D_1}}}{{{D_2}}}\)
A.I,II,III
B.I,III,IV
C.II,III,IV
D.I,II,IV
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