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Consider the planes \(\mathscr{P}\) and \(\mathscr{P}'\) with the following Cartesian equations:$$ \mathscr{P} : x + 2y + 2z - 5 = 0 \quad \text{and} \quad \mathscr{P}' : 2x + z + 1 = 0 $$
  1. Determine a normal vector to each of these two planes.
  2. Deduce their relative position.

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