Chapter 11 - Systems of Equations and Inequalities - 11.3 Systems of Linear Equations: Determinants - 11.3 Assess Your Understanding - Page 744: 70

$v=9i-4j$; magnitude $= \sqrt{97}$

If a vector $v$ initiates at point $P(x_1,y_1)$ and terminates at $Q(x_2,y_2)$ then $v=(x_2-x_1,y_2-y_1)\\ v=(x_2-x_1)i+(y_2-y_1)j$ Hence, here we have $v=[5-(-4)]i+(-1-3)j\\ v=9i-4j$ The magnitude of a vector $v=ai+bj$ is: $||v||=\sqrt{a^2+b^2}$. Hence, $||v||=\sqrt{9^2+(-4)^2}\\ ||v||=\sqrt{81+16}\\ ||v||=\sqrt{97}.$