Two forces $P$ and $Q$, of magnitude $2F$ and $3F$, respectively, are at an angle $\theta $ with each other. If the force $Q$ is doubled, then their resultant also gets doubled. Then, the angle $\theta $ is ....... $^o$

A bus is moving on a straight road towards north with a uniform speed of $50\; km / hour$ then it turns left through $90^{\circ} .$ If the speed remains unchanged after turning, the increase in the velocity of bus in the turning process is

“Explain Triangle method (head to tail method) of vector addition.”

$100$  coplanner forces each equal to  $10\,\,N$  act on a body. Each force makes angle $\pi /50$ with the preceding force. What is the resultant of the forces.......... $N$

The resultant of $\overrightarrow P $ and $\overrightarrow Q $ is perpendicular to $\overrightarrow P $. What is the angle between $\overrightarrow P $ and $\overrightarrow Q $

A person moves $30\, m$ north and then $20\, m$ towards east and finally $30\sqrt 2 \,m$  in south-west direction. The displacement of the person from the origin will be