Answer
$\lt -3,\dfrac{70}{13}\gt$ and $\dfrac{\sqrt{6421}}{13}$
Work Step by Step
The magnitude of a vector is:$|n|=\sqrt{n_1^2+n_2^2}$
Here, $u=\lt 3,-2 \gt; v= \lt -2,5 \gt$
Now,$-\dfrac{5}{13}u +\dfrac{12}{13}v=-\dfrac{5}{13}\lt 3,-2 \gt +\dfrac{12}{13} \lt -2,5 \gt$
or, $ =\lt -3,\dfrac{70}{13} \gt$
$|\lt -3,\dfrac{70}{13}\gt|=\sqrt{(-3)^2+(\dfrac{70}{13})^2}$
or, $|\lt -3,\dfrac{70}{13}\gt|=\dfrac{\sqrt{6421}}{13}$
