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

Following forces start acting on a particle at rest at the origin of the co-ordinate system simultaneously${\overrightarrow F _1} = – 4\hat i – 5\hat j + 5\hat k$, ${\overrightarrow F _2} = 5\hat i + 8\hat j + 6\hat k$, ${\overrightarrow F _3} = – 3\hat i + 4\hat j – 7\hat k$ and ${\overrightarrow F _4} = 2\hat i – 3\hat j – 2\hat k$ then the particle will move

A particle starting from the origin $(0,0)$ moves in a straight line in the $(x, y)$ plane. Its coordinates at a later time are $(\sqrt 3,3)$ . The path of the particle makes with the $x -$ axis an angle of  ……. $^o$

Vector$\overrightarrow A $ makes equal angles with $x, y$ and $z$ axis. Value of its components (in terms of magnitude of $\overrightarrow A $) will be