Dot Product and Work Answers

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?

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

Suppose u · v = 0. Which vectors could represent u and v?

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?

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?

Consider u = ⟨5, –2⟩ and v = ⟨10, –4⟩. What is the relationship between u and v?

Consider vectors u and v, where u = ⟨1, –1⟩ and v = ⟨1, 1⟩. What is the measure of the angle between the vectors?

What is the relationship between vectors u = ⟨3, –1⟩ and v = ⟨6, –2⟩?

Which pair of vectors is orthogonal?

Given u = ⟨3, 2⟩, v = ⟨1, 5⟩, and the angle between the vectors is 45°, what is u · v?