a) \(\overrightarrow{AA'}=\left(0;-2;1\right)\RightarrowĐúng\)
b) \(\overrightarrow{BB'}=\overrightarrow{AA'}=\left(0;-2;1\right)\Rightarrow B'\left(1+0;-2+5;1+1\right)=\left(1;3;2\right)\)
\(\overrightarrow{DD'}=\overrightarrow{AA'}=\left(0;-2;1\right)\Rightarrow D\left(0-0;-2+2;0-1\right)=\left(0;0;-1\right)\)
\(\overrightarrow{AB}=\overrightarrow{DC}=\left(0;3;1\right)\Rightarrow C\left(0+0;3+0;1-1\right)=\left(0;3;0\right)\)
\(\Rightarrow Sai\)
c) \(AB=\sqrt{0^2+3^2+1^2}=\sqrt{10}\)
\(\overrightarrow{CC'}=\overrightarrow{AA'}=\left(0;-2;1\right)\Rightarrow C'\left(0+0;-2+3;1+0\right)=\left(0;1;1\right)\)
\(\overrightarrow{C'A}=\left(1;1;1\right)\Rightarrow C'A=\sqrt{1^2+1^2+1^2}=\sqrt{3}\)
\(\RightarrowĐúng\)
d) Gọi \(M\left(x;y;z\right)\)
\(P=MA^2+MB^2+MC^2+MD^2\) đạt giá trị nhỏ nhất khi \(M\equiv G\) là trọng tâm \(ABCD\) (Tự chứng minh dùng \(\overrightarrow{MA}+\overrightarrow{MB}+\overrightarrow{MC}+\overrightarrow{MD}=4\overrightarrow{MG}\))
\(\Rightarrow M\left(\dfrac{0+1+1+0+0}{4};\dfrac{1+2+5+3+0}{4};\dfrac{1+0+1+0-1}{4}\right)\)
\(\Rightarrow M=\left(\dfrac{2}{4};\dfrac{10}{4};\dfrac{1}{4}\right)=\left(\dfrac{1}{2};\dfrac{5}{2};\dfrac{1}{4}\right)\)
\(\Rightarrow Sai\)
