Question

If $\overline{a}\times \overline{i}+2\overline{a}-4\overline{i}-2\overline{j}+\overline{k}=0$, then $\overline{a}=$

• A. $2\overline{j}+\overline{k}$
• B. $2\overline{j}-\overline{k}$
• C. $2\overline{i}+\overline{j}$
• D. $2\overline{i}-\overline{j}$

Answer 1

The correct option is C $2\overline{i}+\overline{j}$

$\overrightarrow{a}\times \hat{i}+2\overrightarrow{a}-4\hat{i}-2\hat{j}+\hat{k}=\overrightarrow{0}$
$\overrightarrow{a}\times \hat{i}+2\overrightarrow{a}=4\hat{i}+2\hat{j}-\hat{k}$ ---------(1)
$Let\overrightarrow{a}=4\hat{i}+v\hat{j}+\omega \hat{k}$
$\overrightarrow{a}\times \hat{i}=-v\hat{k}+\omega \hat{j}$
$\overrightarrow{a}\times \hat{i}+2\overrightarrow{a}=2u\hat{i}+2v\hat{j}+2\omega \hat{k}-v\hat{k}+\omega \hat{j}$ --------(2)
equate (1) & (2)
$2u=4$ ---------(3)
$2v+\omega =2$ ---------(4)
$2\omega -v=-1$ ----------(5)
$\omega =0v=1u=2$
$\overrightarrow{a}=2\hat{i}+\hat{j}$