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Question
Distance between the two planes: 2x + 3y + 4z = 4 and 4x + 6y + 8z = 12 is
(A) 2 units
(B) 4 units
(C) 8 units
(D)`2/sqrt29 "units"`
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Solution
The equations of the planes are
2x + 3y + 4z = 4 ....(1)
4x + 6y + 8z = 12
`=> 2x + 3y + 4z = 6 ...(2)`
It can be seen that the given planes are parallel.
It is known that the distance between two parallel planes, ax + by + cz = d1 and ax + by+ cz = d2, is given by,
Thus, the distance between the lines `2/sqrt29` units.
Hence, the correct answer is D.
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