Question

If $(2,-1,2)$ is the centroid of tetrahedron $OABC$ and $G_1$ is the centroid of $\Delta ABC$ then $|{\overline{OG}}_1|=$

• A. $4$
• B. $1$
• C. $\frac{9}{2}$
• D. $\frac{3}{2}$

Answer 1

The correct option is A $4$

Centroid of $OABC=\frac{\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}+\overrightarrow{o}}{4}$
$4\times (2,-1,2)=\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}$
Centroid of $\Delta ABC=\frac{\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}}{3}$
$G_1=\frac{4}{3}(2,-1,2)$
$\left|O{G}_1\right|=\frac{4}{3}\sqrt{2^2+1^2+2^2}$
$=4$