Question

A vector $\overrightarrow{r}$ is equally inclined with the coordinate axes. If the tip of $\overrightarrow{r}$ is in the positive octant and $\left|r\right|=6$, 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. $2\sqrt{3}(\hat{i}+\hat{j}+\hat{k})$

Answer 1

Answer: (D)

$2\sqrt{3}(\hat{i}+\hat{j}+\hat{k})$

Let $l,m,n$ be the $D{C}^{\prime }$ s of $r$

Then $l=m=n$ (given).

$\therefore l^2+m^2+n^2=1$

$\Rightarrow 3l^2=1$

$\Rightarrow l=\frac{1}{\sqrt{3}}=m=n$

$\therefore r=\left|r\right|(l\hat{i}+m\hat{j}+n\hat{k})$

$=6(\frac{1}{\sqrt{3}}\hat{i}+\frac{1}{\sqrt{3}}\hat{j}+\frac{1}{\sqrt{3}}\hat{k})$

$=2\sqrt{3}(\hat{i}+\hat{j}+\hat{k}).$