Find the value of λ so that the lines

and 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 equation as in form of

And

So, the Cartesian form is

and

Where

The direction ratio of these lines are -3,2,2 and 3,1, -7

Since the line are perpendicular,

Then using formula (ii)

a₁a₂ + b₁b₂ +c₁c₂ = 0

⇒-3(3λ) +2λ+2(-7) = 0

⇒-9λ+2λ-14 = 0

⇒-7λ = 14

⇒λ = -2