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The direction ratios of a line can be found by subtracting the corresponding coordinates of two points through which the line passes i.e. (subtract x coordinates, subtract y coordinates, subtract z coordinates), this is the direction ratio of the line. There can be no direction ratio of a line passing through only one point, there should be at least two points.

The direction ratios of a line passing through the points (1,–1,2) and (3,4,–2) are,

(3–1,4–{–1},–2–2) = (2,5,–4)

Or it can also be the other way you can choose the first and the second point of your own choice.

The direction ratios of a line passing through the points (0,3,2) and (3,5,6) are,

(3–0,5–3,6–2) = (3,2,4)

The direction ratios of lines are,

(a₁,b₁,c₁) = (2,5,–4)

(a₂,b₂,c₂) = (3,2,4)

By using dot product.

cos θ = 0

θ =

Therefore,, the lines are perpendicular.