A vector v in the first octant is inclined to the x -axis at 60^°, to the y -axis at 45^° and to the z -axis at an acute angle. If a plane passing…

A vector $\displaystyle \vec{v}$ in the first octant is inclined to the $\displaystyle x$-axis at $\displaystyle 60^{\circ}$, to the $\displaystyle y$-axis at $\displaystyle 45^{\circ}$ and to the $\displaystyle z$-axis at an acute angle. If a plane passing through the points $\displaystyle (\sqrt{2},-1,1)$ and $\displaystyle (a, b, c)$, is normal to $\displaystyle \vec{v}$, then