Question

If $\overrightarrow{r}.\hat{i}=\overrightarrow{r}.\hat{j}=\overrightarrow{r}.\hat{k}$ and $\left|\overrightarrow{r}\right|=3,$ then $\overrightarrow{r}=$

• A. $\pm 3(\hat{i}+\hat{j}+\hat{k})$
• B. $\pm \frac{1}{3}(\hat{i}+\hat{j}+\hat{k})$
• C. $\pm \frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})$
• D. $\pm \sqrt{3}(\hat{i}+\hat{j}+\hat{k})$

Answer 1

The correct option is D $\pm \sqrt{3}(\hat{i}+\hat{j}+\hat{k})$

Let $\overrightarrow{r}=x\hat{i}+y\hat{j}+z\hat{k}$.

Since $\overrightarrow{r}.\hat{i}=\overrightarrow{r}.\hat{j}=\overrightarrow{r}.\hat{k}$

$\Rightarrow x=y=z$ ...(1)

Also $\left|\overrightarrow{r}\right|=\sqrt{x^2+y^2+z^2}=3\Rightarrow x=\pm \sqrt{3}$

Hence, the required vector $\overrightarrow{r}=\pm \sqrt{3}(\hat{i}+\hat{j}+\hat{k})$