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

Let $O$ be the origin,$\vec{OP} = \vec{a}$ and $\vec{OQ} = \vec{b}$. If $R$ is a point on $\vec{OP}$ such that $\vec{OP} = 5\vec{OR}$,and $M$ is a point such that $\vec{OQ} = 5\vec{RM}$,then $\vec{PM}$ is equal to:

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

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

Let $\vec{a}, \vec{b}, \vec{c}$ be three non-zero vectors such that no two of them are collinear. If the vector $\vec{a} + 3\vec{b}$ is collinear with $\vec{c}$ and $\vec{b} + 2\vec{c}$ is collinear with $\vec{a}$,then find the value of $\vec{a} + 3\vec{b} + 6\vec{c}$.

Find the position vector of the point on the line passing through the point $\hat{i} - \hat{j} + 2\hat{k}$ and parallel to the vector $3\hat{i} + \hat{j} + \hat{k}$,which is at a distance of $3\sqrt{11}$ units from the point $\hat{i} - \hat{j} + 2\hat{k}$.