Answer
$10$
Work Step by Step
If a vector $v$ initiates at point $P_1(x_1,y_1)$ and terminates at $P_2(x_2,y_2)$ then $v$ is equal to the position vector $v=(x_2-x_1)i+(y_2-y_1)j.$
Hence here: $v=(8\sqrt2-3\sqrt2)i+(2\sqrt2-7\sqrt2)j=5\sqrt2i-5\sqrt2j.$
The magnitude $||v||$ of a vector $v=ai+bj$, can be computed using the formula
$||v||=\sqrt{a^2+b^2}$.
Hence here: $||v||=\sqrt{(5\sqrt2)^2+(-5\sqrt2)^2}=\sqrt{50+50}=\sqrt{100}=10$.