Fundamentals of Physics Extended (10th Edition)

Published by Wiley

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 $\vec{A}$.

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.