If G is centroid of then: - Vidyadip

MCQ

If $G$ is centroid of $\triangle\text{ABC}$ then:

A
$\vec{G}=\vec{a}+\vec{b}+\vec{c}$
B
$\vec{G}=\frac{\vec{a}+\vec{b}+\vec{c}}{2}$
✓
$3 \vec{ G }=\vec{a}+\vec{b}+\vec{c}$
D
$3 \vec{G}=\frac{\vec{a}+\vec{b}+\vec{c}}{2}$

✓

Answer

Correct option: C.

$3 \vec{ G }=\vec{a}+\vec{b}+\vec{c}$

We have,
In a $\triangle\text{ABC}$
$\overrightarrow {\text{A}}=\overrightarrow{\text{a}}$
$\overrightarrow {\text{B}}=\overrightarrow{\text{b}}$
$\overrightarrow {\text{C}}=\overrightarrow{\text{c}}$
then,
we know that,
$\overrightarrow {\text{G}} = \frac {\overrightarrow{\text{a}} + \overrightarrow {\text{b}} +\overrightarrow{\text{c}}}{3}$
$3\overrightarrow {\text{G}}=\overrightarrow {\text{a}}+ \overrightarrow {\text{b}}+\overrightarrow {\text{c}}$

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