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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