Answer
$v=-i+3j$ and $||v||=\sqrt{10}$
Work Step by Step
Let us consider that a vector $v$ is given by: $v=pi+qj$
If a vector $v$ initiates at point $p(x_1,y_1)$ and terminates at $q(x_2,y_2)$, then
$v =\lt x_2-x_1, y_2-y_1 \gt =(x_2-x_1)i+(y_2-y_1) \ j$
The magnitude of a vector can be determined using the formula
$||v||=\sqrt{p^2+q^2} ~~~(1)$
We have: $v=(-1-0)i+[1-(-2)]j=-i+3j$
We will use formula (1) to obtain:
$||v||=\sqrt{(-1)^2+(3)^2}\\
=\sqrt{1+9}\\
=\sqrt{10}$
