Find the angle between the vectors a = î − 2ĵ + 3k̂ and b = 3î − 2ĵ + k̂.

Find the angle between the vectors a = î − 2ĵ + 3k̂ and b = 3î − 2ĵ + k̂.

• A. cos⁻¹(5/7)
• B. cos⁻¹(10/14)
• C. cos⁻¹(5/14)
• D. Both A and B

Answer: D) Both A and B

Explanation: a.b = 3 + 4 + 3 = 10. |a| = √(1+4+9) = √14. |b| = √(9+4+1) = √14. cos(θ) = (a.b) / (|a||b|) = 10 / 14 = 5/7. Thus, cos⁻¹(5/7) and cos⁻¹(10/14) are the same.