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 points with position vectors $60\,i + 3\,j$,$40\,i - 8\,j$,and $a\,i - 52\,j$ are collinear,if $a = $

If $\vec{a} = 4\hat{i} + 3\hat{j}$ and $\vec{b} = 2\hat{i} + \lambda\hat{j}$ are parallel vectors,then the value of $\lambda$ is:

In the given figure,which of the vectors are collinear?

If $ABCDEF$ is a regular hexagon with $\vec{AB} = \vec{a}$ and $\vec{BC} = \vec{b}$,then $\vec{CE}$ equals to

Let $\vec{a}, \vec{b},$ and $\vec{c}$ be three non-zero vectors such that no two of them are collinear. If the vector $\vec{a} + 2\vec{b}$ is collinear with $\vec{c}$ and $\vec{b} + 3\vec{c}$ is collinear with $\vec{a}$,then $\vec{a} + 2\vec{b} + 6\vec{c} = \dots$