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, we know that the direction ratios of the line segment joining (x₁, y₁, z₁) and (x₂, y₂, z₂) is taken as x₂ – x₁, y₂ – y₁, z₂ – z₁ (or x₁ – x₂, y₁ – y₂, z₁ – z₂).

⇒ The direction ratios of the line through the points (1, –1, 2) and (3, 4, –2) is:

a₁ = 3 – 1 = 2, b₁ = 4 – (-1) = 4 + 1 = 5, c₁ = -2 –2 = -4

and the direction ratios of the line through the points (0, 3, 2) and (3, 5, 6) is:
a₂ = 3 – 0 = 3, b₂ = 5 – 3 = 2, c₂ = 6 – 2 = 4

Now, consider

a₁a₂ + b₁b₂ + c₁c₂ = 2 × 3 + 5 × 2 + (-4) × 4 = 6 + 10 + (-16) = 16 + (-16) = 0

⇒ The line through the points (1, –1, 2), (3, 4, –2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).