Show that the lines 
and 
are perpendicular to each other.
The Cartesian equation of the lines are 
and 
and we need to find that weather the lines are perpendicular or not, so we will use the dot product equation, as we know the direction ratios of both the lines.
a1a2+b1b2+c1c2 = (7)(1) + (–5)(2) + (1)(3) = 7 – 10 + 3 = 0
Hence the given lines are perpendicular because,
cos θ = 0
θ = 
19