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Show that a x+b y+r=0,b y+c z+p=0a n dc ...

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.

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The planes `a_(1)x+b_(1)y+c_(1)z+d_(1)=0 and a_(2)x+b_(2)y +c_(2)z +d_(2)=0` are perpendicular to each other if and only if `a_(1)a+b_(1)b+c_(1)c=0`.
The equation of `x-y, y-z, and z-x` planes are `z=0, x=0 and y=0`, respectively.
Now we have to show that `z=0` is perpendicular to `ax+by+r=0`.
It follows immediately, since `a(0)+b(0)+(0)(1)=0`, other parts can be done similarlhy.
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