methinks there's a misprint in the sum it shud be aa' + cc' = -1
it goes this way...
x=ay+b or y = x - ba
z=cy+d or y = z - dc
so we get the first line as:
x - ba = y = z - dc
.
.
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similarly.........
x - b'a' = y = z - d'c'
so D.R of first line is < a, 1 , c>
and that of 2nd line is < a' , 1 , c' >
for them to be perpendicular
aa' + 1 + cc' = 0
or aa' + cc' = -1