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Câu hỏi: Trong không gian $Oxyz,$ cho hai điểm $A\left( 1;-2;-1 \right),B\left( 1;2;2 \right).$ Phương trình mặt cầu tâm A, bán kính AB là
A. ${{\left( x-1 \right)}^{2}}+{{\left( y+2 \right)}^{2}}+{{\left( z+1 \right)}^{2}}=5.$
B. ${{\left( x-1 \right)}^{2}}+{{\left( y-2 \right)}^{2}}+{{\left( z-1 \right)}^{2}}=25.$
C. ${{\left( x-1 \right)}^{2}}+{{\left( y+2 \right)}^{2}}+{{\left( z+1 \right)}^{2}}=25.$
D. ${{\left( x-1 \right)}^{2}}+{{\left( y-2 \right)}^{2}}+{{\left( z-2 \right)}^{2}}=5.$
A. ${{\left( x-1 \right)}^{2}}+{{\left( y+2 \right)}^{2}}+{{\left( z+1 \right)}^{2}}=5.$
B. ${{\left( x-1 \right)}^{2}}+{{\left( y-2 \right)}^{2}}+{{\left( z-1 \right)}^{2}}=25.$
C. ${{\left( x-1 \right)}^{2}}+{{\left( y+2 \right)}^{2}}+{{\left( z+1 \right)}^{2}}=25.$
D. ${{\left( x-1 \right)}^{2}}+{{\left( y-2 \right)}^{2}}+{{\left( z-2 \right)}^{2}}=5.$
Ta có $\overrightarrow{AB}=\left( 0;4;3 \right)\Rightarrow AB=5\Rightarrow \left( S \right):{{\left( x-1 \right)}^{2}}+{{\left( y+2 \right)}^{2}}+{{\left( z+1 \right)}^{2}}=25.$ Chọn C.
Đáp án C.