The two lines ax+by+c=0 and a'x+b'y+c'=0...

The two lines `ax+by+c=0` and `a'x+b'y+c'=0` are perpendicular if (i) `ab'=a'b` (ii) `ab+a'b'=0` (iii) `ab'+a'b=0` (iv) `a a'+b b'=0`

`aa'+bb=0`

`ab'=ba'`

`ab+a'b'=0`

`ab'+ba'=0`

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