If G is centroid of then: - Vidyadip

MCQ

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

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

✓

Answer

Correct option: C.

$3\overrightarrow {\text{G}}=\overrightarrow {\text{a}}+ \overrightarrow {\text{b}}+\overrightarrow {\text{c}}$

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,
$\overrightarrow {\text{G}} = \frac {\overrightarrow{\text{a}} + \overrightarrow {\text{b}} +\overrightarrow{\text{c}}}{3}$
$3\overrightarrow {\text{G}}=\overrightarrow {\text{a}}+ \overrightarrow {\text{b}}+\overrightarrow {\text{c}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from INTRODUCTION TO THREE DIMENSIONAL GEOMETRY→INTRODUCTION TO THREE DIMENSIONAL GEOMETRY — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $f(x)=\left\{\begin{array}{ll}\sin x, & x \neq n \pi, \quad n \in I \\ 2, & \text { otherwise }\end{array}\right.$ and $g(x)=\left\{\begin{array}{ll}x^{2}+1, & x \neq 0,2 \\ 2, & x=0 \\ 4, & x=2\end{array}\right.$ then $\lim _{x \rightarrow 0}$$g[f(x)]$ is

If $P(B) = \frac{3}{4}$, $P(A \cap B \cap \bar C) = \frac{1}{3}{\rm{ }}$ and $P(\bar A \cap B \cap \bar C) = \frac{1}{3},$ then $P(B \cap C)$ is

What is number of outcomes when tossing two coins together?

The minimum value of $3\sin \theta + 4\cos \theta $ is

If $\tan \,n\theta = \tan m\theta $, then the different values of $\theta $ will be in

Let U be the universal set containing 700 elements. If A, B are subsets of U such that $\text{n(A)}=200,\text{ n(B)}=300$ and $\text{n(A}\cap\text{B)}=100.$ Then, $\text{n(A}'\cap\text{B}')=$

Latus rectum of the parabola ${y^2} - 4y - 2x - 8 = 0$ is

If $(\alpha ,\beta )$ is a point on the circle whose centre is on the $x -$ axis and which touches the line $x + y = 0$ at $(2, -2)$, then the greatest value of $\alpha$ is

If ${^\text{15}}\text{C}_{3\text{r}}={^\text{15}}\text{C}_{\text{r+3}},$ is then equal to:

The area of the triangle with vertices $A ( z ), B ( iz )$ and $C(z+i z)$ is