$A$ unit vector which is in the opposite direction of $(2, -2, 1)$ is $........$

The points with position vectors $10\,i + 3\,j$,$12\,i - 5\,j$,and $a\,i + 11\,j$ are collinear,if $a = $

If $a = i + 2j + 3k$,$b = -i + 2j + k$ and $c = 3i + j$,then the unit vector along their resultant is:

If a vector $a$ of magnitude $50$ is collinear with the vector $b = 6i - 8j - \frac{15}{2}k$, and makes an acute angle with the positive direction of the $z$-axis, then the vector $a$ is equal to:

If the sum of two unit vectors is a unit vector,then the magnitude of their difference is

Let $\overrightarrow{OA} = \hat{i} - 3\hat{j} + \hat{k}$, $\overrightarrow{OB} = \hat{i} + 3\hat{j} - 2\hat{k}$, and $\overrightarrow{OC} = 4\hat{i} + 3\hat{j} + 5\hat{k}$ be the position vectors of three points $A$, $B$, and $C$. Let $P$ be the point which divides $AB$ in the ratio $2:1$. If $l, m, n$ are the direction cosines of the vector $\overrightarrow{PC}$, then $l + 3m + 2n =$