A vector \(\vec{v}\) in the first octant is inclined to the \(x\)-axis at \(60^{\circ}\), to the \(y\)-axis at \(45^{\ci…

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