Find the distance between the planes and [CBSE 2016]

Given:

plane 1: 2x - 3y + 6z – 4 = 0 and

plane 2: 6x - 9y + 18z + 30 = 0

General form for equation of plane is given by ax + by + cz + d

Now comparing the co - efficient of x, y and z for both the planes

Ratio of co - efficient of x =

The ratio of the coefficient of y =

The ratio of the coefficient of z =

Now since all the ratios are equal, we can say that both the planes are parallel to each other

Arbitrarily selecting a point which lies on plane 1, let’s say (x₁, y_1, z₁) which is (2, 0, 0)

Now the distance between the planes is given by

Formula:

Substituting the values in the above equation

Hence, the distance between the given planes is 2 units.