Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 3 - Vectors - Questions: 6b

Answer

At least one of the vectors $\vec{a}, \vec{b}$ must be the zero vector.

Work Step by Step

Consider some real number $a, b$. Then $a+b = a-b$ is only true when at least one number equals to 0. Similarly, in a vector space, the equality holds only if $\vec{a}$, $\vec{b}$, or both is the additive identity (i.e.) the zero vector.
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