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 $\vec P$
$\frac {6}{\sqrt 5}$
$\frac {8}{\sqrt 5}$
$\frac {12}{\sqrt 5}$
$\frac {16}{\sqrt 5}$
A displacement vector of magnitude $4$ makes an angle $30^{\circ}$ with the $x$-axis. Its rectangular components in $x-y$ plane are .........
Which of the following statement$(s)$ is are correct?
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
The projection of a vector $\vec r\, = \,3\hat i\, + \,\hat j\, + \,2\hat k$ on the $xy$ plane has magnitude