The magnitudes of pairs of displacement vectors are given. Which pair of displacement vectors cannot be added to give a resultant vector of magnitude $13 \, cm$?

The planes of two rigid discs are perpendicular to each other. They are rotating about their axes. If their angular velocities are $3 \, rad/s$ and $4 \, rad/s$ respectively,then the resultant angular velocity of the system would be ........ $rad/s$.

$A$ vector $\vec Q$ which has a magnitude of $8$ is added to the vector $\vec P$ which lies along the $x$-axis. The resultant of the two vectors lies along the $y$-axis and has a magnitude twice that of $\vec P$. The magnitude of $\vec P$ is:

Two forces of magnitudes $3 \ N$ and $4 \ N$ act on an object. If the angle between them is $180^\circ$,then their resultant force is ......... $N$.

The vector sum of two forces is perpendicular to their vector difference. In that case,the forces

$A$ force of $6\,N$ and another of $8\,N$ can be applied together to produce the effect of a single force of $..........\,N$