Given: - Two lines having vector notion and

The position vectors of arbitrary points on the given lines are

1^st line

2^nd line

If the lines intersect, then they must have a common point.

Therefore for some value of λ and μ, we have

⇒ (2λ + 1) = μ + 2, – 1 = μ – 1, λ = – μ

⇒ 2λ – μ = 1 ……(i)

⇒ μ = 0 ……(ii)

and λ = μ ……(iii)

from eq ii and eq iii we get

⇒ λ = 0 and μ = 0

As we can see by putting the value of λ and μ in eq i, that it does not satisfy the equation.

Check

⇒ 2λ – μ = 1

⇒ 2(0) – (0) = 1

⇒ 0 = 1

⇒ LHS≠RHS ;Hence intersection point exist or line does not intersects