If $\overline{e}_1, \overline{e}_2$ and $\overline{e}_1+\overline{e}_2$ are unit vectors,then the angle between $\overline{e}_1$ and $\overline{e}_2$ is (in $^{\circ}$)

The direction ratios of the line bisecting the angle between the $x$-axis and the line having direction ratios $(3, -1, 5)$ are

If the position vectors of three points are $a$,$b$,and $(3a - 2b)$,then these points are .....

If $\overline{a} = \bar{i} - 2\bar{j} + 2\bar{k}$ and $\overline{b} = 9\bar{i} + 6\bar{j} - 18\bar{k}$ are two vectors, then $\frac{\text{Projection of } \overline{b} \text{ on } \overline{a}}{\text{Projection of } \overline{a} \text{ on } \overline{b}} = $

If the position vectors of $A$ and $B$ are respectively $(1, 1, 0)$ and $(0, 1, 1)$,then $\overrightarrow{AB} =$

Three forces of magnitudes $1, 2, 3 \text{ dynes}$ meet at a point and act along the diagonals of three adjacent faces of a cube. The resultant force is ............ $\text{dyne}$.