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

Two vectors $\overrightarrow a $ and $\overrightarrow b $ are at an angle of $60^o$ with  each other. Their resultant makes an angle of $45^o$ with $\overrightarrow a $ . If $|\overrightarrow b | = 2\,units$ then $|\overrightarrow a |$ is:-

For the given vector $\vec A =3\hat i -4\hat j+10\hat k$ , the ratio of magnitude of its component on the $x-y$ plane and the component on $z-$ axis is

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

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to $\overrightarrow{\mathrm{A}}$ and its magnitude is half that of $\vec{B}$. The angle between vectors $\vec{A}$ and $\vec{B}$ is . . . . . . 

Two vectors of magnitude $3$ & $4$ have resultant which make angle $\alpha$ & $\beta$ respectively with them $\{given\, \alpha + \beta \neq 90^o\}$