21 The triangle inequality says: (length of v + w) ≤ (length of v) + (length of w). Problem 19 found ||v + w||² = ||v||² +2v • w+ ||w||². Use the Schwarz inequality v • w ≤ ||v|| ||w|| to show that || side 3|| can not exceed ||side 1|| + ||side 2||: ||v + w|| ² ≤ (||v|| + ||w||) ² or ||v+w|≤||v|| + ||w||. Triangle inequality

21 The triangle inequality says: (length of v + w) ≤ (length of v) + (length of w). Problem 19 found ||v + w||² = ||v||² +2v • w+ ||w||². Use the Schwarz inequality v • w ≤ ||v|| ||w|| to show that || side 3|| can not exceed ||side 1|| + ||side 2||: ||v + w|| ² ≤ (||v|| + ||w||) ² or ||v+w|≤||v|| + ||w||. Triangle inequality

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterA: Appendix

SectionA.3: Inequalities

Problem 9E

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