Question Detail
Question
Find the angle between two vectors A = 2i + 3j + 4k and B = i - 2j + 3k.
Correct Answer
Option B is the correct answer.
Detailed Explanation
The angle θ between two vectors is given by cosθ = (A·B)/(|A||B|). A·B = (2)(1) + (3)(-2) + (4)(3) = 2 - 6 + 12 = 8. |A| = √(2² + 3² + 4²) = √(4 + 9 + 16) = √29 ≈ 5.385. |B| = √(1² + (-2)² + 3²) = √(1 + 4 + 9) = √14 ≈ 3.742. cosθ = 8/(5.385 × 3.742) = 8/20.15 = 0.397. θ = cos⁻¹(0.397) = 66.6°.
Hint
Use the dot product formula: A·B = |A||B|cosθ.