What is the minimum number of coplanar vectors having different magnitudes that can be added to give a zero resultant?

$A$ car travels a distance of $6 \, km$ at an angle of $45^\circ$ with the East,and then travels a distance of $4 \, km$ at an angle of $135^\circ$ with the East. What is the distance from the origin?

The angle between vector $\vec{Q}$ and the resultant of $(2 \vec{Q} + 2 \vec{P})$ and $(2 \vec{Q} - 2 \vec{P})$ is:

The direction cosines of vector $(A - B)$,if $A = 2\hat{i} + 3\hat{j} + \hat{k}$ and $B = 2\hat{i} + 2\hat{j} + 3\hat{k}$,are:

The unit vector parallel to the resultant of the vectors $\vec A = 4\hat i + 3\hat j + 6\hat k$ and $\vec B = - \hat i + 3\hat j - 8\hat k$ is

If $\vec{A} + \vec{B} = \vec{C}$ and $A + B = C$,what is the angle between $\vec{A}$ and $\vec{B}$?