Find the value of so that the following lines are perpendicular to each other.

Formula: -

(i)in Cartesian form of the lines

And

(ii) Two line with direction ratio and are perpendicular if then

Given: -

And

Arranging the above

and

Arranging the above equation as in form of

And

So, the Cartesian form is

Where x₁ = 5, x₂ = 0, y₁ = 2, y₂ = - �, z₁ = 1,z₂ = 1,

a₁ = 5λ+2, a₂ = 1, b₁ = -5, b₂ = 2λ,c₁ = 1,c₂ = 3

The direction ratio of these lines are and5λ+2, -5,1 and 1, 2λ ,3

Since the line are perpendicular

Then using formula (ii)

a₁a₂ + b₁b₂ +c₁c₂ = 0

⇒(5λ+2)(1)+(-5)(2λ)+1(3) = 0

⇒5λ+2-10λ+3 = 0

⇒-5λ = -5

⇒λ = 1