The displacement of a particle from a point having position vector $2 \hat{i} + 4 \hat{j}$ to another point having position vector $5 \hat{i} + 1 \hat{j}$ is ........ units.

The magnitude of the vector sum of two forces $10 \ N$ and $6 \ N$ cannot be ......... $N$.

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

The sum of two forces $\overrightarrow{P}$ and $\overrightarrow{Q}$ is $\overrightarrow{R}$ such that $|\overrightarrow{R}| = |\overrightarrow{P}|$. The angle $\alpha$ (in degrees) that the resultant of $2\overrightarrow{P}$ and $\overrightarrow{Q}$ will make with $\overrightarrow{Q}$ is

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 ........ $rad/s$.

If the magnitudes of vectors $\vec P$,$\vec Q$,and $\vec R$ are $5$,$12$,and $13$ units respectively,and if $\vec P + \vec Q = \vec R$,then the angle between $\vec Q$ and $\vec R$ is: