Mark the correct alternative in the following:
The distance between the planes 2x + 2y – z + 2 = 0 and 4x + 4y – 2z + 5 = 0 is
We know that, distance between two parallel planes:
Ax + By + Cz + D1=0…… (1) and Ax + By + Cz + D2=0…… (2) is given by,
Here, the two parallel planes are given as,
2x + 2y - z + 2=0 …………… (3)
and 4x + 4y - 2z + 5=0 i.e. 2x + 2y - z + =0 ………… (4)
Comparing equation (3) with equation (1) and equation (4) with equation (2) we get,
A=2, B=2, C= - 1, D1=2 and D2=.
So, the distance between the given two parallel planes are,
Hence, the distance between the parallel planes 2x + 2y - z + 2=0 and 4x + 4y - 6z + = is .