Trong không gian với hệ trục \(Oxyz\) , cho mặt cầu \(\left( S \right):{{\left( x-1 \right)}^{2}} {{\left( y 2 \right)}^{2}} {{\left( z-3 \right)}^{2}}=12\) và mặt phẳng \(\left( P \right):2x 2y-z-3=0\) . Viết phương trình mặt phẳng \(\left( Q \right)\) song song với \(\left( P \right)\) và cắt \(\left( S \right)\) theo thiết diện là đường tròn \(\left( C \right)\) sao cho khối nón có đỉnh là tâm mặt cầu và đáy là đường tròn \(\left( C \right)\) có thể tích lớn nhất .
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