If $a = 3i - 2j + k$,$b = 2i - 4j - 3k$ and $c = -i + 2j + 2k$,then $a + b + c$ is

The points with position vectors $\bar{a}+\bar{b}$,$\bar{a}-\bar{b}$,and $\bar{a}+k\bar{b}$ are collinear:

If $a$ and $b$ are two vectors such that $a \cdot b = 0$ and $a \times b = 0$,then:

$A$ vector coplanar with the non-collinear vectors $\vec{a}$ and $\vec{b}$ is:

If $\bar{a}, \bar{b}, \bar{c}$ are three non-zero vectors,no two of them are collinear,$\bar{a}+2 \bar{b}$ is collinear with $\bar{c}$,and $\bar{b}+3 \bar{c}$ is collinear with $\bar{a}$,then $\bar{a}+2 \bar{b}$ is equal to:

If the position vectors of points $A, B, C$ are respectively $\hat{i}, \hat{j}, \hat{k}$ and $\vec{AB} = \vec{CX}$,then the position vector of point $X$ is: