Question

Show that the lines (x-5)/7 =(y+2)/-5=z/1 and x/1=y/2=z/3 are perpendicular to each other.

Answer 1

The direction ratios of the given lines are 7, −5, 1 and 1, 2, 3 respectively.
Two lines with direction ratios, a₁, b₁, c₁ and a₂, b_2, c₂, are perpendicular to each other,
if a₁a₂ + b₁ b₂ + c₁c₂ = 0
7 × 1 + (−5) × 2 + 1 × 3
= 7 − 10 + 3
= 0

Therefore, the given lines are perpendicular to each other.