Practice Triangle Inequality (27.6) - Inner Product Spaces

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6 sample questions

Question 1.
State the Triangle Inequality for vectors u and v.
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Think about the vector norms.
Question 2.
If u = (3, 4) and v = (6, 8), what are ||u|| and ||v||?
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Use the Pythagorean theorem to find these lengths.
3Question 3.
What does the Triangle Inequality state?
- ||u - v|| < ||u|| + ||v||
- ||u + v|| ≥ ||u|| + ||v||
- ||u + v|| ≤ ||u|| + ||v||
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Think about the lengths of vectors.
4Question 4.
The Triangle Inequality holds true for all inner product spaces.
- True
- False
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Is this a general rule or an exception?
Question 5.
Given vectors u = (3, 1) and v = (-1, 4), prove the Triangle Inequality using their norms.
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First find the result of u + v, then calculate the norms.
Question 6.
Prove or disprove: If ||u|| > 0 and ||v|| > 0, then ||u + v|| > ||u|| + ||v||?
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Consider the definition and properties of norms.

4 more questions in this section. Enroll free to practise them all.