If a particle moves from point $P (2,3,5)$ to point $Q (3,4,5)$. Its displacement vector be

Two vectors $\vec A$ and $\vec B$ have equal magnitudes. The magnitude of $(\vec A + \vec B)$ is $‘n’$ times the magnitude of $(\vec A - \vec B)$. The angle between $ \vec A$ and $\vec B$ is

The resultant of two vectors $\overrightarrow P $ and $\overrightarrow Q $ is $\overrightarrow R .$ If $Q$ is doubled, the new resultant is perpendicular to $P$. Then $R $ equals

An object of $m\, kg$ with speed of $v\, m/s$ strikes a wall at an angle $\theta$ and rebounds at the same speed and same angle. The magnitude of the change in momentum of the object will be

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 ....... $^o$

The resultant of two vectors $A$ and $B$ is perpendicular to the vector $A$ and its magnitude is equal to half the magnitude of vector $B$. The angle between $A$ and $B$ is ....... $^o$