Let $\overline{OA}=\overline{a}, \overline{OB}=\overline{b}$. If the vector along the angle bisector of $\angle AOB$ is given by $x \frac{\overline{a}}{|\overline{a}|}+y \frac{\overline{b}}{|\overline{b}|}$,then which of the following is true?

The position vector of a point lying on the line joining the points whose position vectors are $\hat{i}+\hat{j}-\hat{k}$ and $\hat{i}-\hat{j}+\hat{k}$ is:

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 $m + n =$

The position vectors of $P$ and $Q$ are respectively $\overrightarrow{a}$ and $\overrightarrow{b}$. If $R$ is a point on the line $PQ$ such that $\overrightarrow{PR}=5 \overrightarrow{PQ}$,then the position vector of $R$ is

If $\vec{a}$ is a nonzero vector of magnitude $a$ and $\lambda$ is a nonzero scalar,then $\lambda \vec{a}$ is a unit vector if

If $M_1, M_2, M_3$ and $M_4$ are respectively the magnitudes of the vectors $\vec{a}_1 = 2\hat{i} - \hat{j} + \hat{k}$,$\vec{a}_2 = -3\hat{i} - 4\hat{j} - 4\hat{k}$,$\vec{a}_3 = -\hat{i} + \hat{j} - \hat{k}$,and $\vec{a}_4 = -\hat{i} + 3\hat{j} + \hat{k}$,then the correct order of $M_1, M_2, M_3$ and $M_4$ is: