Find the angle between the line r = (i + 2j − k) + λ(i − j + k) and the line r = (2i − j + k) + μ(2i + j + 2k).

Find the angle between the line r = (i + 2j − k) + λ(i − j + k) and the line r = (2i − j + k) + μ(2i + j + 2k).

• A. cos⁻¹(1/3)
• B. cos⁻¹(√3/9)
• C. sin⁻¹(1/3)
• D. cos⁻¹(1/√3)

Answer: B) cos⁻¹(√3/9)

Explanation: b₁ = i − j + k, b₂ = 2i + j + 2k. b₁·b₂ = 2 − 1 + 2 = 3. |b₁| = √3, |b₂| = 3. cos θ = 3 / (3√3) = 1/√3. 1/√3 is not among the main distinct values unless simplified. Option D is cos⁻¹(1/√3), which is correct. Oh, 1/√3 is the answer.