Đặt \(A\left(0;0;0\right)\)
a) \(\overrightarrow{BC}=C\left(a;a;0\right)-B\left(a;0;0\right)=\left(0;a;0\right)\)
\(\overrightarrow{BC'}=C'\left(a;a;a\right)-B\left(a;0;0\right)=\left(0;a;a\right)\)
\(cos\left(\widehat{\overrightarrow{BC};\overrightarrow{BC'}}\right)=\dfrac{a^2}{a.a\sqrt{2}}=\dfrac{1}{\sqrt{2}}\Rightarrow\left(\widehat{\overrightarrow{BC};\overrightarrow{BC'}}\right)=45^o\Rightarrow\) Đúng
b) \(\overrightarrow{AC}=C\left(a;a;0\right)-A\left(0;0;0\right)=\left(a;a;0\right)\)
\(\overrightarrow{B'D'}=D'\left(0;a;a\right)-B'\left(a;0;a\right)=\left(-a;a;0\right)\)
\(cos\left(\widehat{\overrightarrow{AC};\overrightarrow{B'D'}}\right)=\dfrac{-a^2+a^2}{a.\sqrt{2}a\sqrt{2}}=0^o\Rightarrow\left(\widehat{\overrightarrow{AC};\overrightarrow{B'D'}}\right)=90^o\Rightarrow\) Sai
c) \(\left|\overrightarrow{OO'}\right|=\sqrt{\left(\dfrac{a}{2}-\dfrac{a}{2}\right)^2+\left(\dfrac{a}{2}-\dfrac{a}{2}\right)^2+\left(0-a\right)^2}=a\)
\(\Rightarrow\) Đúng
d) \(\left|\overrightarrow{OB'}\right|=\sqrt{\left(\dfrac{a}{2}-a\right)^2+\left(\dfrac{a}{2}-0\right)^2+\left(0-a\right)^2}=a\sqrt{\dfrac{3}{2}}\)
\(\Rightarrow\) Sai
