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 planes defined by \( x - y = 0 \), \( y - z = 0 \), and \( z - x = 0 \) respectively, we can follow these steps:

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

The normal vector of a plane given by the equation \( Ax + By + Cz = D \) is \( \vec{n} = (A, B, C) \).

1. For the plane \( ax + by + r = 0 \):
- Normal vector \( \vec{n_1} = (a, b, 0) \)
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