3
AssignmentMultiple Choice

Dot Product and Work

Question 3 • Precalculus

Find the angle θ between u = 〈6, –5〉 and v = 〈11, 8〉.

Answer
A
θ = 3.77°
B
θ = 75.83°
C
θ = 89.87°
D
θ = 165.83°

Explanation

Use the dot product formula: cos θ = (u · v) / (|u||v|). Here, u · v = 6(11) + (−5)(8) = 26, and |u||v| = √61√185, so θ = cos⁻¹(26/(√61√185)) ≈ 75.83°. Therefore, the angle is 75.83° (choice B).

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