Question Detail

The angle θ between two vectors is given by cos θ = (A·B)/(|A||B|). A·B = (3)(2) + (-4)(-6) + (-2)(3) = 6 + 24 - 6 = 24. |A| = √(3² + (-4)² + (-2)²) = √(9 + 16 + 4) = √29 ≈ 5.385. |B| = √(2² + (-6)² + 3²) = √(4 + 36 + 9) = √49 = 7. cos θ = 24/(5.385 × 7) = 24/37.695 ≈ 0.6367. θ = cos⁻¹(0.6367) ≈ 50.4°. This doesn't match 134.4°. If we compute 24/(5.385×7) = 24/37.695 = 0.637, arccos = 50.4°. But 134.4° is 180° - 45.6°, so maybe dot product is negative? Recalculate: 3×2=6, (-4)×(-6)=+24, (-2)×3=-6, total=24 positive. So angle <90°. Possibly the given options have 134.4° as the larger angle, but the correct acute angle is about 50.4°. Perhaps the vectors are different or I misread.