Show that the lines and are perpendicular to each other.

The Cartesian equation of the lines are and , as we know their direction ratios we can find weather they are perpendicular or not, for proving the lines to be perpendicular we can only consider the numerator of the dot product when we use cos θ = numerator

cos θ = 7×1 + 2×(–5) + 1×3

cos θ = 7 – 10 + 3

cos θ = 0

θ =

Therefore, the lines are perpendicular.