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  4. Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

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Q. Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is

AIEEEAIEEE 2004

Solution:

Given planes are
$2x + y + 2z − 8 = 0,\, 4x + 2y + 4z + 5 = 0 ⇒ 2x + y + 2z + 5/2 = 0$
Distance between planes $= \frac{\left|d_{1}-d_{2}\right|}{\sqrt{a^{2}+b^{2}+c^{2}}} = \frac{\left|-8-5/2\right|}{\sqrt{2^{2}+1^{2}+2^{2}}} = \frac{7}{2}.$