If $a = 2i + 5j$ and $b = 2i - j,$ then the unit vector along $a + b$ will be

If the position vector of one end of the line segment $AB$ is $2\hat{i} + 3\hat{j} - \hat{k}$ and the position vector of its midpoint is $3\,(\hat{i} + \hat{j} + \hat{k}),$ then the position vector of the other end is

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

The perimeter of the triangle whose vertices have the position vectors $\hat{i}+\hat{j}+\hat{k}$,$5\hat{i}+3\hat{j}-3\hat{k}$,and $2\hat{i}+5\hat{j}+9\hat{k}$ is

The position vectors of $A$ and $B$ are $2i - 9j - 4k$ and $6i - 3j + 8k$ respectively. Then the magnitude of $\overrightarrow{AB}$ is:

The vectors $3i + j - 5k$ and $ai + bj - 15k$ are collinear if $....$