The angles which a vector $\hat i + \hat j + \sqrt 2 \,\hat k$ makes with $X, Y$ and $Z$ axes respectively are
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 $\vec P$