With respect to a fixed origin O, the lines L₁ and L₂ are given by the equations: L₁: r = ⟨1, 2, -1⟩ + λ⟨-2, 1, 3⟩ L₂: r = ⟨-1, 1, 4⟩ + μ⟨0, 1, -1⟩ (a) Show that the lines L₁ and L₂ do not intersect.

Mark scheme

Marking points from the official mark scheme. The mark or mark type is shown in brackets.

1. M1 for equating components of r for L₁ and L₂ to form three equations.
2. A1 for correctly forming the equations: 1 - 2λ = -1, 2 + λ = 1 + μ, -1 + 3λ = 4 - μ.
3. M1 for solving two equations simultaneously for λ and μ.
4. A1 for showing that values of λ and μ obtained from two equations do not satisfy the third equation, leading to the conclusion that the lines do not intersect.