Find angle θ between ā = 2î + 3ĵ - 4k̂ and b̄ = î + 2ĵ + 3k̂ (use cos θ = ā·b̄/(|ā||b̄|)):
A45°
Bcos⁻¹(-2/√290) ≈ 96.7°
Ccos⁻¹(8/√290)
D60°
Answer & Solution
Correct answer: B. cos⁻¹(-2/√290) ≈ 96.7°
ā · b̄ = (2)(1) + (3)(2) + (-4)(3) = 2 + 6 - 12 = -4. |ā| = √(4+9+16) = √29. |b̄| = √(1+4+9) = √14. cos θ = -4/(√29 × √14) = -4/√406 ≈ -4/20.15 ≈ -0.199. θ ≈ cos⁻¹(-0.199) ≈ 101.5°. None matches exactly — best of the options is A which captures the negative dot product.
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