ABC is an equilateral triangle. Length of each side is a and centroid is point O . Find overri

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3-1.Vectors

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$ABC$ is an equilateral triangle. Length of each side is $a$ and centroid is point $O$. Find $\overrightarrow{A B}+\overrightarrow{A C}=n \overrightarrow{A O}$ then $n = ........ $

A

$0$

B

$1$

C

$2$

D

$3$

Solution

$\overrightarrow{A B}=\overrightarrow{A O}+\overrightarrow{O B}$ and

$\overrightarrow{A C}=\overrightarrow{A O}+\overrightarrow{O C}$

$\therefore \overrightarrow{A B}+\overrightarrow{A C}=2 \overrightarrow{A O}+\overrightarrow{O B}+\overrightarrow{O C} \ldots$ (1)

but $\overrightarrow{O A}+\overrightarrow{O B}+\overrightarrow{O C}=\overrightarrow{0}$

$\therefore \overrightarrow{O B}+\overrightarrow{O C}=-\overrightarrow{O A}=\overrightarrow{A O} \ldots$ (2)

by $(1)$ and $(2)$

$\overrightarrow{A B}+\overrightarrow{A C}=2 \overrightarrow{A O}+\overrightarrow{A O}$

$\overrightarrow{A B}+\overrightarrow{A C}=3 \overrightarrow{A O} \therefore n=3$

Standard 11

Physics

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