Show that the lines are perpendicular to each other.

We know that

Two lines with direction ratios a₁, b₁, c₁ and a₂, b₂, c₂ are perpendicular if the angle between them is θ = 90°, i.e. a₁a₂ + b₁b₂ + c₁c₂ = 0

Also, here the direction ratios are:

a₁ = 7, b₁ = -5, c₁ = 1 and a₂ = 1, b₂ = 2, c₂ = 3

Now, Consider

a₁a₂ + b₁b₂ + c₁c₂ = 7 × 1 + (-5) × 2 + 1 × 3 = 7 -10 + 3 = - 3 + 3 = 0

∴ The two lines are perpendicular to each other.