Show that `a x+b y+r=0,b y+c z+p=0a n dc z+a x+q=0` are perpendicular to `x-y ,y-za n dz-x` planes, respectively.

Explanation

To show that the planes given by the equations \( ax + by + r = 0 \), \( by + cz + p = 0 \), and \( cz + ax + q = 0 \) are perpendicular to the \( xy \)-plane, \( yz \)-plane, and \( zx \)-plane respectively, we can use the condition for perpendicularity of planes.

### Step 1: Identify the normal vectors of the given planes

The normal vector of a plane given by the equation \( A x + B y + C z + D = 0 \) is \( \vec{n} = (A, B, C) \).

- For the plane \( ax + by + r = 0 \), the normal vector is \( \vec{n_1} = (a, b, 0) \).
- For the plane \( by + cz + p = 0 \), the normal vector is \( \vec{n_2} = (0, b, c) \).
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