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

If $\hat{i}, \hat{j}, \hat{k}$ are unit vectors,then which of the following is true?

Given vectors $\vec{a} = 2 \hat{i} - \hat{j} + 2 \hat{k}$ and $\vec{b} = -\hat{i} + \hat{j} - \hat{k}$. The vector in the direction of $\vec{a} + \vec{b}$ with magnitude $\sqrt{2}$ is . . . . . . .

Find the unit vector in the direction of the sum of the vectors $\vec{a}=2 \hat{i}-\hat{j}+2 \hat{k}$ and $\vec{b}=-\hat{i}+\hat{j}+3 \hat{k}$.

If $\overline{a} = m \overline{b} + n \overline{c}$,where $\overline{a} = 4 \hat{i} + 13 \hat{j} - 18 \hat{k}$,$\overline{b} = \hat{i} - 2 \hat{j} + 3 \hat{k}$,and $\overline{c} = 2 \hat{i} + 3 \hat{j} - 4 \hat{k}$,then $m + n =$

$a$ and $b$ are two non-collinear vectors,then $xa + yb$ (where $x$ and $y$ are scalars) represents a vector which is