Question

lf $\overline{a},\overline{b},\overline{c}$ are three non-coplanar vectors such that $\overline{b}\times \overline{c}=\overline{a},\overline{c}\times \overline{a}=\overline{b}$ and $\overline{a}\times \overline{b}=\overline{c}$, then $|\overline{a}+\overline{b}+\overline{c}|=$

• A. $1$
• B. $2$
• C. $3$
• D. $\sqrt{3}$

Answer 1

The correct option is D $\sqrt{3}$

Let $\overrightarrow{a}=\hat{i}\overrightarrow{b}=\hat{j}\overrightarrow{c}=\hat{k}$

According to ques the vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ should satisfy given condition

$\overrightarrow{b}\times \overrightarrow{c}=\overrightarrow{a}$

$\hat{j}\times \hat{k}=\hat{i}$ It is true so cindition satisfying

$\overrightarrow{c}\times \overrightarrow{a}=\overrightarrow{b}$

$\hat{k}\times \hat{i}=\hat{j}$

$\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{c}$

$\hat{i}\times \hat{j}=\hat{k}$

So condition is satisfying Now claculate $|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}|$

$|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}|=|\hat{i}+\hat{j}+\hat{k}|$

$|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}|=\sqrt{1^2+1^2+1^2}$

$|\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}|=\sqrt{3}$