$A$ zero vector has

The position vector of a point at a distance of $3\sqrt{11}$ units from $i - j + 2k$ on a line passing through the points $i - j + 2k$ and $3i + j + k$ is

The vectors $a = 2\hat{i} + 3\hat{j} + 6\hat{k}$ and $b$ are collinear and $|b| = 21$,then $b =$

If $a = i - 2j$ and $b = 2i + \lambda j$ are parallel,then $\lambda$ is

If a vector $\vec{r}$ makes equal angles with the axes $OX, OY,$ and $OZ$,find the total number of such vectors $\vec{r}$.

If $\bar{a}=2 \hat{i}-\hat{j}+\hat{k}$,$\bar{b}=\hat{i}+\hat{j}-2 \hat{k}$ and $\bar{c}=4 \hat{i}-2 \hat{j}+\hat{k}$,then the unit vector in the direction of $3 \bar{a}+\bar{b}-2 \bar{c}$ is