$A$ zero vector has

$A$ vector which bisects the angle between $a = 3 \hat{i} - 4 \hat{k}$ and $b = 5 \hat{j} + 12 \hat{k}$ is

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?

Let $ABCD$ be a quadrilateral. If $E$ and $F$ are the midpoints of the diagonals $AC$ and $BD$ respectively and $(\overrightarrow{AB}-\overrightarrow{BC})+(\overrightarrow{AD}-\overrightarrow{DC})= k \overrightarrow{FE}$,then $k$ is equal to

Find the unit vector in the direction of the sum of the vectors,$\vec{a}=2 \hat{i}+2 \hat{j}-5 \hat{k}$ and $\vec{b}=2 \hat{i}+\hat{j}+3 \hat{k}$.

If $P \hat{i}-2 \hat{j}+3 \hat{k}$,$2 \hat{i}+3 \hat{j}-4 \hat{k}$,and $4 \hat{i}+13 \hat{j}-18 \hat{k}$ are the position vectors of three collinear points $A$,$B$,and $C$ respectively,then the vector in the direction of $AB$ of length $|P|$ units is