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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
State the Triangle Inequality for vectors u and v.
💡 Hint: Think about the vector norms.
Question 2
Easy
If u = (3, 4) and v = (6, 8), what are ||u|| and ||v||?
💡 Hint: Use the Pythagorean theorem to find these lengths.
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 does the Triangle Inequality state?
- ||u - v|| < ||u|| + ||v||
- ||u + v|| ≥ ||u|| + ||v||
- ||u + v|| ≤ ||u|| + ||v||
💡 Hint: Think about the lengths of vectors.
Question 2
The Triangle Inequality holds true for all inner product spaces.
- True
- False
💡 Hint: Is this a general rule or an exception?
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given vectors u = (3, 1) and v = (-1, 4), prove the Triangle Inequality using their norms.
💡 Hint: First find the result of u + v, then calculate the norms.
Question 2
Prove or disprove: If ||u|| > 0 and ||v|| > 0, then ||u + v|| > ||u|| + ||v||?
💡 Hint: Consider the definition and properties of norms.
Challenge and get performance evaluation