Diện tích tam giác OBC biết B(1;0;2),C(−2;0;0) là:A.căn 5 B.4 C.2căn 5

Ta có:$\overrightarrow{OB}=\left(1;0;2\right),\overrightarrow{OC}=\left(-2;0;0\right)$

$\Rightarrow \left[\overrightarrow{OB},\overrightarrow{OC}\right]=\left(\left|\begin{array}{cc}\begin{array}{l}0\\ 0\end{array}& \begin{array}{l}2\\ 0\end{array}\end{array}\right|;\left|\begin{array}{cc}\begin{array}{l}2\\ 0\end{array}& \begin{array}{l}1\\ -2\end{array}\end{array}\right|;\left|\begin{array}{cc}\begin{array}{l}1\\ -2\end{array}& \begin{array}{l}0\\ 0\end{array}\end{array}\right|\right)=\left(0;-4;0\right)$

Do đó$S_{OBC}=\frac{1}{2}\left|\left[\overrightarrow{OB},\overrightarrow{OC}\right]\right|=\frac{1}{2}\sqrt{0+{\left(-4\right)}^2+0^2}=2$

Đáp án cần chọn là: D