The  angle between the planes $ x + y + 2z = 9 $and $2x - y +z =15$, is

$\frac{\pi}{6}$ $\frac{\pi}{3}$ $\frac{\pi}{4}$ none of these

$\frac{\pi}{3}$

Let $\theta $ between the planes $x+y+ 2z = 9 $ and $ 2x - y + z = 15.$ Then, $cos \theta = \frac{(1)(2)+(1)(-1)+(2)(1)}{\sqrt{1^2+1^2+2^2}\sqrt{2^2+(-1)^2+1^2}}=\frac{1}{2}⇒ \theta = \frac{\pi}{3}$