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Find the distance between the planes 2x - y + 3z + 4 = 0 and 6x - 3y + 9z - 3 = 0 ?

  4. None of these

Answer (Detailed Solution Below)

Option 1 :
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Detailed Solution

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CONCEPT:

Distance between two parallel planes ax + by + cz + d1 = 0 and ax + by + cz + d2 = 0 is given by: 

CALCULATION:

Here, we have to find the between the planes 2x - y + 3z + 4 = 0 and 6x - 3y + 9z - 3 = 0

The plane 6x - 3y + 9z - 3 = 0 can be re-written as 2x - y + 3z - 1 = 0

So, the planes 2x - y + 3z + 4 = 0 and 2x - y + 3z - 1 = 0 are parallel

As we know that, distance between two parallel planes ax + by + cz + d1 = 0 and ax + by + cz + d2 = 0 is given by: 

Here, d1 = 4, d2 = - 1, a = 2, b = - 1 and c = 3

So, the distance between the given parallel planes is 

Hence, option A is the correct answer.

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