In the following cases, find the distance of each of the given points from the corresponding given plane. Point Plane(a) `(0, 0, 0)` `3x- 4y + 12 z = 3` (b) `(3, -2, 1)` `2x y + 2z + 3 = 0` (c) `(2, 3,-5)` `x+2y-2z=9` (d)`(-6,0,0)` `2x-3y+6z-2=0`

Explanation

To find the distance of each given point from the corresponding plane, we will use the formula for the distance \( D \) from a point \( (x_1, y_1, z_1) \) to a plane given by the equation \( Ax + By + Cz + D = 0 \):

\[ D = \frac{|Ax_1 + By_1 + Cz_1 + D|}{\sqrt{A^2 + B^2 + C^2}} \]

We will apply this formula to each part of the question.

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