Question

A vector $\overrightarrow{r}$ is equally inclined with the coordinate axes. If the tip of $\overrightarrow{r}$ is in the first octant and $|\overrightarrow{r}|=\sqrt{3}$ then $\overrightarrow{r}$ is

• A. $2\sqrt{3}(\hat{i}-\hat{j}+\hat{k})$
• B. $2\sqrt{3}(-\hat{i}+\hat{j}+\hat{k})$
• C. $2\sqrt{3}(\hat{i}+\hat{j}-\hat{k})$
• D. $(\hat{i}+\hat{j}+\hat{k})$

Answer 1

The correct option is D $(\hat{i}+\hat{j}+\hat{k})$

$\overrightarrow{r}=\lambda \hat{i}+\beta \hat{j}+\gamma \hat{k}$
$\overrightarrow{r}\cdot \hat{i}=\overrightarrow{r}\cdot \hat{j}=\overrightarrow{r}\cdot \hat{k}$
$\lambda =\beta =\gamma$
$\left|\overrightarrow{r}\right|=\sqrt{3{\lambda }^2}$
$\lambda =1$
$\overrightarrow{r}=\hat{i}+\hat{j}+\hat{k}$