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: 12


$||v||=4.41$. \begin{bmatrix} \frac{1.12}{4.41} \\ \frac{-3.25}{4.41} \\ \frac{2.07}{4.41} \\ \frac{-1.83}{4.41} \\ \end{bmatrix}

Work Step by Step

I know that for the vector $v=\begin{bmatrix} v_{1} \\ v_{2} \\ \vdots\\ v_{n} \end{bmatrix}$ The unit vector in the direction of $v$ is $\frac{v}{||v||}$. Hence: $||v||=\sqrt{1.12^2+(-3.25)^2+2.07^2+(-1.83)^2}=\sqrt{1.2544+10.5625+4.2849+3.3489}=\sqrt{19.4507}\approx4.41$. Thus, the unit vector in the direction of $v$ is: \begin{bmatrix} \frac{1.12}{4.41} \\ \frac{-3.25}{4.41} \\ \frac{2.07}{4.41} \\ \frac{-1.83}{4.41} \\ \end{bmatrix}
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