Answer
$\lt \dfrac{1}{5},\dfrac{14}{5}\gt$ and $\dfrac{\sqrt{197}}{5}$
Work Step by Step
The formula to find the magnitude of a vector is:
$|n|=\sqrt{n_1^2+n_2^2}$
Here, $\dfrac{3}{5}u +\dfrac{4}{5}v=\dfrac{3}{5}\lt 3,-2 \gt +\dfrac{4}{5} \lt -2,5 \gt =\lt \dfrac{1}{5},\dfrac{14}{5} \gt$
and $|\lt \dfrac{1}{5},\dfrac{14}{5}\gt|=\sqrt{(\dfrac{1}{5})^2+(\dfrac{14}{5})^2}=\dfrac{\sqrt{197}}{5}$
Hence, our final answers are: $\lt \dfrac{1}{5},\dfrac{14}{5}\gt$ and $\dfrac{\sqrt{197}}{5}$
