Linear Algebra: A Modern Introduction

Published by Cengage Learning
ISBN 10: 1285463242
ISBN 13: 978-1-28546-324-7

Chapter 1 - Vectors - 1.2 Length and Angle: The Dot Product - Exercises 1.2 - Page 290: 13

Answer

$\sqrt{17}$

Work Step by Step

I know that for the vector $v=\begin{bmatrix} v_{1} \\ v_{2} \\ \vdots\\ v_{n} \end{bmatrix}$ $||v||=\sqrt{v_1^2+v_2^2+...+v_n^2}$ The distance of two vectors $u$ and $v$ is: $d=||u-v||$. Hence: $d=||\begin{bmatrix} -1 \\ 2 \\ \end{bmatrix}-\begin{bmatrix} 3 \\ 1 \\ \end{bmatrix}||=||\begin{bmatrix} -4 \\ 1 \\ \end{bmatrix}||=\sqrt{(-4)^2+1^2}=\sqrt{16+1}=\sqrt{17}$
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.