If the system of equations $$x + (\sqrt{2}\sin\alpha)y + (\sqrt{2}\cos\alpha)z = 0$$, $$x + (\cos\alpha)y + (\sin\alpha)z = 0$$, $$x + (\sin\alpha)y - (\cos\alpha)z = 0$$ has a non-trivial solution, then $$\alpha \in \left(0,\frac{\pi}{2}\right)$$ is equal to:

A

$$\frac{11\pi}{24}$$

B

$$\frac{5\pi}{24}$$

C

$$\frac{7\pi}{24}$$

D

$$\frac{3\pi}{4}$$