Show that the lines and are perpendicular to each other.

Question

Philoid · Accepted Answer

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 =