Why can't vectors be added algebrically?

University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter2: Vectors
Section: Chapter Questions
Problem 22CQ: If the cross product of two vectors vanishes, what can you say about their directions?
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Why can't vectors be added algebrically?

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