## Linear Algebra: A Modern Introduction

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