The zero vector $(0,0,0)$ $........$

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

If the vectors $\vec{AB} = -3\hat{i} + 4\hat{k}$ and $\vec{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}$ are the sides of a $\triangle ABC$,then the length of the median through $A$ is

If $a, b$ and $c$ are three vectors such that $|a|=|b|=2$,$a \cdot b=2$ and $a+b+c=0$,then $|c|$ is equal to

The unit vector parallel to the resultant vector of $2i + 4j - 5k$ and $i + 2j + 3k$ is

If $P, Q, R$ are the mid-points of the sides $AB, BC$ and $CA$ of $\triangle ABC$ respectively,then $PC - BQ =$