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

If the vector $19 \hat{i}+22 \hat{j}+5 \hat{k}$ bisects an angle between the vectors $a$ and $6 \hat{i}+8 \hat{j}$,then the unit vector in the direction of $a$ is

If $a = \hat{i} + 4 \hat{j}$,$b = 2 \hat{i} - 2 \hat{j}$,and $c = 5 \hat{i} + 9 \hat{j}$,then $c$ is equal to:

If the position vectors of two points $A$ and $B$ are $\vec{a} + 3\vec{b}$ and $\vec{a} - 2\vec{b}$ respectively,find the position vector of the point that divides $AB$ in the ratio $2:5$.

If $\vec{r} = 3\hat{i} + 2\hat{j} - 5\hat{k}$,$\vec{a} = 2\hat{i} - \hat{j} + \hat{k}$,$\vec{b} = \hat{i} + 3\hat{j} - 2\hat{k}$,and $\vec{c} = -2\hat{i} + \hat{j} - 3\hat{k}$ such that $\vec{r} = \lambda\vec{a} + \mu\vec{b} + \gamma\vec{c}$,then -

If $G$ is the centroid of the $\triangle ABC$,then $\vec{GA} + \vec{GB} + \vec{GC}$ is equal to