# 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, 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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Find the coordinate of the point P where the line through and crosses the plane passing through three points and Also, find the ratio in which P divides the line segment AB.

Mathematics - Board Papers