Practice Triangle Inequality (27.6) - Inner Product Spaces - Mathematics (Civil Engineering -1)
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Triangle Inequality

Practice - Triangle Inequality

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Practice Questions

Test your understanding with targeted questions

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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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?

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

Prove or disprove: If ||u|| > 0 and ||v|| > 0, then ||u + v|| > ||u|| + ||v||?

💡 Hint: Consider the definition and properties of norms.

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