Consider vectors u = ⟨2, 1⟩ and v = ⟨4, –1⟩ with the angle between them equal to 40°. What are the scalar projections uv and vu?

The scalar projection of u onto v is |u| cos 40°. Since |u| = √(2² + 1²) = √5, this is approximately √5 cos 40° = 1.71. The scalar projection of v onto u is |v| cos 40°; |v| = √(4² + (−1)²) = √17, giving approximately √17 cos 40° = 3.16. Thus choice D, uv = 1.71 and vu = 3.16, is correct.

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