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: 6c

Answer

Any $\vec{a}$ and $\vec{b}$ that are perpendicular to each other

Work Step by Step

Notice that the second constraint is the Pythagorean theorem which suggests that we should think about right triangles. Indeed, if $\vec{a}$ and $\vec{b}$ are perpendicular to each other, their vector sum $\vec{c}$ is the hypotenuse of the triangle. For example, let $\vec{a} = <0, 3> $and $\vec{b} = <4,0>$, then $\vec{a} + \vec{b} = \vec{c} = <4,3>$ and $|a| = 3, |b| = 4,$ and $|c| = 5$ 3-4-5 is a Pythagorean triple.
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