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: 10a

Answer

$\vec{B}$ and $\vec{C}$ have the same dot product with $\vec{A}$ $\vec{D}$ and $\vec{E}$ also have the same dot product with $\vec{A}$

Work Step by Step

Recall the definition of a dot product $\vec{a} \cdot \vec{b} = |a| |b| cos(\phi)$ Since all four vectors have the same length, the product of the norms ($|a| |b|$ part of the formula) is the same for all four. What is different is the angle $\theta$. Cosine is positive in the I and IV quadrants, hence $\vec{B}$ and $\vec{C}$ have the same dot product with $\vec{A}$. Similarly, cosine is negative in the II and III quadrants, so $\vec{D}$ and $\vec{E}$ also have the same dot product with $\vec{A}$.
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