If $C$ is the midpoint of $\overline{AB}$ and $P$ is any point not on $\overline{AB}$,then which of the following is true?

The position vector of point $C$ relative to $B$ is $(\hat{i} + \hat{j})$ and the position vector of $B$ relative to $A$ is $(\hat{i} - \hat{j})$. The position vector of $C$ relative to $A$ is:

If $2\vec{a} - 3\vec{b}$,$\vec{b}$,and $\vec{a} - \vec{b}$ are the position vectors of three points $A$,$B$,and $C$ respectively,then they are:

If $a$ and $b$ are two vectors such that $a \cdot b = 0$ and $a \times b = 0$,then:

If $A(2, 3, 5)$,$B(1, 2, 3)$,$C(-5, 4, -2)$,and $D(1, 10, 10)$,then ...

$R$ divides the line joining two points $P$ and $Q$ whose position vectors are $\hat{i}+2 \hat{j}-\hat{k}$ and $-\hat{i}+\hat{j}+\hat{k}$ respectively in the ratio $2: 1$ externally. $S$ divides $PQ$ internally in the ratio $2: 1$. Then,the position vector of the midpoint of the line joining $R$ and $S$ is