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Distance between Two Parallel Planes

The distance ...

Question

The distance between two parallel planes 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is

A

2 units

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B

units

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C

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D

8 units

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Solution

The correct option is C

Planes are 4x + 6y + 8z = 8

4x + 6y + 8z = 12

$d i s t a n c e = \frac{| d_{1} - d_{2} |}{\sqrt{a^{2} + b^{2} + c^{2}}} = \frac{| 12 - 18 |}{\sqrt{16 + 36 + 64}} = \frac{4}{\sqrt{116}} = \frac{2}{\sqrt{29}}$

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Similar questions

Q. Distance between the two planes :

2 x + 3 y + 4 z = 4

4 x + 6 y + 8 z = 12

Q. Distance between the parallel planes

2 x - 3 y + 4 z - 1 = 0

4 x - 6 y + 8 z + 8 = 0

Distance between the two planes: and is

(A)2 units (B)4 units (C)8 units

(D)

units

) between the parallel planes

2 x - 3 y + 4 z - 1 = 0

4 x - 6 y + 8 z + 7 = 0

Q. The distance between the planes

2 x + 3 y + 4 z = 4

4 x + 6 y + 8 z = 12

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