Dot Product and Work Answers

Given vectors u = ⟨–3, 2⟩ and v = ⟨2, 1⟩, what is the measure of the angle between the vectors?

A force of 10 newtons acts in a direction 75° above horizontal, moving an object 15 meters from (0, 0) to (15, 0). What is the work done by the force?

Which pair of vectors is orthogonal?

Given vectors u and v, with |u| = 10 and |v| = 12, and the angle between the vectors is 53°, what is u · v?

Given vectors u = ⟨2, –3⟩ and v = ⟨1, –1⟩, what is the measure of the angle between the vectors?

Suppose vector u = , |v| = 6, and the angle between the vectors is 120°. What is u · v?

What is the relationship between vectors u = ⟨1, 0⟩ and v = ⟨0, –3⟩?

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?

A force acts in the direction ⟨4, 2⟩, moving an object along a straight path from (2, –4) to (10, 1). How much work is done by the force?

Given u = ⟨1, 3⟩, v = ⟨2, 1⟩, and cos(ϴ) = , where ϴ is the angle between the vectors, what is the scalar projection uv and the dot product u · v?