Classify the following physical quantity as a scalar or a vector:
$10 \, g/cm^3$

If the direction cosines of a vector of magnitude $3$ are $\frac{2}{3}, -\frac{1}{3}, \frac{2}{3}$,then the vector is:

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 $2:5$.

Two vectors $u$ and $v$ are parallel if and only if

If $\overrightarrow {AO} + \overrightarrow {OB} = \overrightarrow {BO} + \overrightarrow {OC} ,$ then $A, B, C$ form

Let $ABCD$ be a parallelogram and $2\hat{i}+\hat{j}$,$4\hat{i}+5\hat{j}+4\hat{k}$ and $-\hat{i}-4\hat{j}-3\hat{k}$ be the position vectors of the vertices $A$,$B$,and $D$ respectively. Then the position vector of one of the points of trisection of the diagonal $AC$ is