Chapter 7 - Section 7.5 - Vectors: An Algebraic Approach - 7.5 Problem Set - Page 404: 33

$|W|=\sqrt{5}.$

The magnitude of a vector is given by the possible square root of the sum of the squares of its horizontal and vertical components. We have $W=i+2j.$ Then \begin{align*} |U|&=\sqrt{(1)^{2}+(2)^{2}}\\ &=\sqrt{1+4}\\ &=\sqrt{5}. \end{align*} Hence, $|W|=\sqrt{5}.$