Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 12: Vectors and the Geometry of Space - Section 12.3 - The Dot Product - Exercises 12.3 - Page 712: 18

Answer

Both two vectors $\overrightarrow{CA}$ and $\overrightarrow{CB}$ are orthogonal.

Work Step by Step

Let $\overrightarrow{CA}$ and $\overrightarrow{CB}$ be the two vectors. Now, $(-v+(-u)) \cdot (-v+u)=v \cdot v-v \cdot u+u \cdot v -u \cdot u$ and $v \cdot v-v \cdot u+u \cdot v -u \cdot u=|v|^2-|u|^2$ when the both vectors posses same radius of circle then we have $|v|^2 =|u|^2$ This implies that $|v|^2-|u|^2=|v|^2-|v|^2=0$ Hence, we conclude that both two vectors $\overrightarrow{CA}$ and $\overrightarrow{CB}$ are orthogonal.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

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.