If three unit vectors overrightarrow{a}, over | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given,the condition is $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$ ...$(i)$ Since $\overrightarrow{a}, \overrigh

Vedclass · Accepted Answer

$\frac{2 \pi}{3}$

Vedclass · Answer

(A) Given,the condition is $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$ ...$(i)$ Since $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ are unit vectors,we have $|\overrightarrow{a}|=|\overrightarrow{b}|=|\overrightarrow{c}|=1$. Let the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ be $	heta$. From equation $(i)$,we can write: $\overrightarrow{a}+\overrightarrow{b}=-\overrightarrow{c}$ Squaring both sides,we get: $(\overrightarrow{a}+\overrightarrow{b})^2=(-\overrightarrow{c})^2$ $|\overrightarrow{a}|^2+|\overrightarrow{b}|^2+2(\overrightarrow{a} \cdot \overrightarrow{b})=|\overrightarrow{c}|^2$ Substituting the values $|\overrightarrow{a}|=1, |\overrightarrow{b}|=1, |\overrightarrow{c}|=1$: $1^2+1^2+2(\overrightarrow{a} \cdot \overrightarrow{b})=1^2$ $2+2(\overrightarrow{a} \cdot \overrightarrow{b})=1$ $2(\overrightarrow{a} \cdot \overrightarrow{b})=-1$ $\overrightarrow{a} \cdot \overrightarrow{b}=-\frac{1}{2}$ Using the definition of the dot product,$\overrightarrow{a} \cdot \overrightarrow{b}=|\overrightarrow{a}||\overrightarrow{b}| \cos 	heta$: $1 \cdot 1 \cdot \cos 	heta = -\frac{1}{2}$ $\cos 	heta = -\frac{1}{2}$ Since $\cos 	heta = -\frac{1}{2}$,the angle $	heta = \frac{2 \pi}{3}$.

If three unit vectors $\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}$ satisfy $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}$,then the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is

Similar Questions

The molecule having one unpaired electron is

Which one of the following oxides is reduced by water gas to obtain the metal during its extraction?

Which of the following orders is correct for the heat of hydrogenation of these compounds?

$A$ solid reflects incident light and its electrical conductivity decreases with temperature. The binding in this solid is:

Which process is used for the removal of hardness of water?

Vedclass Test Series

Exam Paper Generator

Online Exam Module