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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

COMEDKCOMEDK 2013Three Dimensional Geometry

Solution:

The planes are $4x + 2y + 4z = 16, 4x + 2y + 4z = -5$
Distance between planes = $\frac{16-\left(-5\right)}{\sqrt{4^{2}+2^{2}+4^{2}}}=\frac{21}{6}=\frac{7}{2}$