A plane is revolving around the earth with a speed of $100\, km/hr $ at a constant height from the surface of earth. The change in the velocity as it travels half circle is.........$km/hr$

The resultant of $\vec A$ and $\vec B$ makes an angle $\alpha $ with $\vec A$ and $\beta $ with $\vec B$,

A particle is situated at the origin of a coordinate system. The following forces begin to act on the particle simultaneously (Assuming particle is initially at rest)

${\vec F_1} = 5\hat i - 5\hat j + 5\hat k$            ${\vec F_2} = 2\hat i + 8\hat j + 6\hat k$

${\vec F_3} =  - 6\hat i + 4\hat j - 7\hat k$         ${\vec F_4} =  - \hat i - 3\hat j - 2\hat k$

Then the particle will move

A body is moving under the action of two forces ${\vec F_1} = 2\hat i - 5\hat j\,;\,{\vec F_2} = 3\hat i - 4\hat j$. Its velocity will become uniform under an additional third force ${\vec F_3}$ given by

If the sum of two unit vectors is also a unit vector. then magnitude of their difference and angle between the two given unit vectors is ..............

If $\vec{P}+\vec{Q}=\vec{P}-\vec{Q}$, then