## Precalculus (10th Edition)

$v=2i-4j$ $||v||=2\sqrt5$
If a vector $v$ initiates at point $P(x_1,y_1)$ and terminates at $Q(x_2,y_2)$ then $v==(x_2-x_1)i+(y_2-y_1)j.$ Hence, here $v=(3-1)i+[-6-(-2)]j\\ v=2i-4j$ The magnitude of a vector $v=ai+bj$ is: $||v||=\sqrt{a^2+b^2}$. Thus, $||v||=\sqrt{2^2+(-4)^2}=\sqrt{4+16}=\sqrt{20}=2\sqrt5$