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?

If $2 \overrightarrow{a} + 3 \overrightarrow{b} - 5 \overrightarrow{c} = \overrightarrow{0}$,then the ratio in which $\overrightarrow{c}$ divides $\overrightarrow{AB}$ is

$A$ and $B$ are two points. The position vector of $A$ is $6b - 2a$. $A$ point $P$ divides the line segment $AB$ in the ratio $1 : 2$. If $a - b$ is the position vector of $P$,then the position vector of $B$ is given by:

Classify the following measure as a scalar or a vector:
$10^{-19} \text{ Coulomb}$

If $\hat{i}+4 \hat{j}+3 \hat{k}$,$\hat{i}+2 \hat{j}+3 \hat{k}$,and $3 \hat{i}+2 \hat{j}+\hat{k}$ are position vectors of $A$,$B$,and $C$ respectively,and if $D$ and $E$ are midpoints of sides $BC$ and $AC$,then $\overrightarrow{DE}$ is equal to:

Let the position vectors of the vertices $A, B$ and $C$ of a triangle be $2 \hat{i}+2 \hat{j}+\hat{k}$,$\hat{i}+2 \hat{j}+2 \hat{k}$ and $2 \hat{i}+\hat{j}+2 \hat{k}$ respectively. Let $l_1, l_2$ and $l_3$ be the lengths of perpendiculars drawn from the orthocenter of the triangle on the sides $AB, BC$ and $CA$ respectively,then $l_1^2+l_2^2+l_3^2$ equals: