Find the position vector of a point A in space such that $\overrightarrow{OA}$ is inclined at $60^{\circ}$ to OX and at $45^{\circ}$ to OY and $\mid \overrightarrow{OA}\mid$=10 units.

Question

$\begin{array}{1 1} \hat i + \sqrt 2 \hat j + \hat k \\ 5\hat i + 5\sqrt 2 \hat j - 5 \hat k \\ 10\hat i + 10\sqrt 2 \hat j + 10 \hat k \\ 5\hat i + 5\sqrt 2 \hat j + 5 \hat k\end{array} $