Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - 13.2 Vectors in Three Dimensions - Exercises - Page 659: 24

Answer

${\bf{u}}$ and ${\bf{v}}$ are parallel.

Work Step by Step

${\bf{u}}$ and ${\bf{v}}$ are parallel if there exists some scalar $\lambda $ such that ${\bf{u}} = \lambda {\bf{v}}$. So, $\left( {1, - 2,5} \right) = \lambda \left( { - 2,4, - 10} \right)$ $1 = - 2\lambda $, ${\ \ }$ $ - 2 = 4\lambda $, ${\ \ }$ $5 = - 10\lambda $. From the first equation we obtain $\lambda = - \frac{1}{2}$. This value satisfies the second and the third equation. Therefore, ${\bf{u}}$ and ${\bf{v}}$ are parallel.
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.