Write the distance between the parallel planes 2x – y + 3z = 4 and 2x – y + 3z = 18.
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–y + 3z=4 i.e. 2x–y + 3z - 4=0 …………… (3)
and 2x–y + 3z=18 i.e. 2x–y + 3z - 18=0 ………… (4)
Comparing equation (3) with equation (1) and equation (4) with equation (2) we get,
A=2, B= - 1, C=3, D1= - 4 and D2= - 18.
So, the distance between the given two parallel planes are,
Hence, the distance between the parallel planes 2x–y + 3z=4 and 2x–y + 3z=18 is .