Planes

Geometry Level pending

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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