Find the distance between the planes $2 x + 2 y + z + 3 = 0$ and $2 x + 2 y + z - 15 = 0$

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Solution

$2 x + 2 y + z + 3 = 0$
$2 x + 2 y + z - 15 = 0$
distance between planes
$\frac{| d_{1} - d_{2} |}{\sqrt{a^{2} + b^{2} + c^{2}}} = \frac{| 3 - (- 15) |}{\sqrt{2^{2} + 2^{2} + 1^{2}}}$
$= \frac{18}{3}$
$= 6$

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