A vector $\vec{r}$ is inclined at equal angles to OX, OY and OZ. If the magnitude of $\vec{r}$ is 6 units, then $\vec{r}$ =
Answer & explanation
Correct answer: option 2
Let l, m, n be the direction cosines of $\vec{r}$ which is equally inclined to the coordinates axes. Then,
$∴ l = m = n = ±\frac{1}{\sqrt{3}}$
Hence, $\vec{r}= |\vec{r}|(l\hat{i}+m\hat{j}+n\hat{k})$
$⇒\vec{r}= 6\begin{Bmatrix} ±\frac{1}{\sqrt{3}}\hat{i}±\frac{1}{\sqrt{3}}\hat{j}±\frac{1}{\sqrt{3}}\hat{k}\end{Bmatrix}= 2\sqrt{3} (± \hat{i} ± \hat{j}± \hat{k})$