Chapter 7 - Section 7.5 - Vectors: An Algebraic Approach - 7.5 Problem Set - Page 404: 34

$|W|=\sqrt{10}.$

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 $W=3i+j.$ Then \begin{align*} |U|&=\sqrt{(3)^{2}+(3)^{2}}\\ &=\sqrt{9+1}\\ &=\sqrt{10}. \end{align*} Hence, $|W|=\sqrt{10}.$