Q. 73.5( 4 Votes )

Find the distance between the planes and [CBSE 2016]

Answer :

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, y1, 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.

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