Question

Let L₁: (x – x₁)/a₁ = (y – y₁)/b₁ = (z – z₁)/c₁

and L₂: (x – x₂)/a₂ = (y – y₂)/y₂ = (z – z₂)/c₂

are perpendicular or, if a₁a₂ + b₁b₂ + c₁c₂ = 0

and parallel if a₁/a₂ = b₁/b₂ = c₁/c₂ 

If the lines L₁ : x = ay + b, z = cy + d and L₂ : x = x'y + b', z = c'y + d' are perpendicular, then

(a) aa' + cc' = 0

(b) aa' + cc' = –1

(c) aa' – cc' = 0

(d) aa' – cc' = 1 

Answer 1

Answer is (b) aa' + cc' = –1

Since L₁ and L₂ are perpendicular, so sum of the product of their sirection ratios is zero.

Thus, a.a' + 1.1 + c.c' = 0 

aa' + cc' = –1.