# Planes

Geometry Level 3

Consider the represented planes:

$$\alpha$$: $${ b }^{ 2 }x+y+z=bx$$

$$\beta$$: $$2x+y=-2-z$$

$$\gamma$$: $$x+b(y+z)=0$$

$$b \in \mathbb{R}$$ $$\diagdown$${0}

$$\cdot$$ $$\alpha$$ and $$\beta$$ are strictly parallel.

$$\cdot$$ $$\gamma$$ intersects $$\alpha$$ and $$\beta$$, but it isn't perpendicular to them.

What is the value of $$b$$?

###### This problem was created by José Carlos Pereira
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