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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
State the formula for the projection of vector u onto vector v.
💡 Hint: Think about how we express one vector in the direction of another.
Question 2
Easy
What does the inner product ⟨u, v⟩ represent?
💡 Hint: It's related to the angle between the vectors.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the formula for projecting vector u onto vector v?
- proj_v(u) = (⟨u
- v⟩ / ⟨u
- u⟩) u
- proj_v(u) = (⟨u
- v⟩ / ⟨v
- v⟩) v
- proj_u(v) = (⟨v
- u⟩ / ⟨u
- u⟩) u
💡 Hint: Remember the correct order of vectors in the projection formula.
Question 2
True or False: The projection of a vector can exceed the original vector's magnitude.
- True
- False
💡 Hint: Consider what projection represents in terms of direction.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given vectors u = (2, 3) and v = (1, 4), determine the projection of u onto v and the significance of this projection.
💡 Hint: First compute the inner products.
Question 2
In a physical context, how can the projection of force onto a support beam help to determine safety evaluations?
💡 Hint: Think about how forces interact with structural designs.
Challenge and get performance evaluation