First slide

Planes in 3D

Question

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

Moderate

A

$\frac{3}{2}$
B

$\frac{9}{2}$
C

$\frac{7}{2}$
D

$\frac{5}{2}$

Solution

Given planes are $4 x + 2 y + 4 z - 16 = 0, 4 x + 2 y + 4 z + 5 = 0$
Distance between the parallel planes $= \frac{| d_{1} - d_{2} |}{\sqrt{a^{2} + b^{2} + c^{2}}} = \frac{7}{2}$

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