Answer
$\lt -3,\dfrac{70}{13}\gt$ and $\dfrac{\sqrt{6421}}{13}$
Work Step by Step
The formula to find the magnitude of a vector is:
$|n|=\sqrt{n_1^2+n_2^2}$
Here, $-\dfrac{5}{13}u +\dfrac{12}{13}v=-\dfrac{5}{13}\lt 3,-2 \gt +\dfrac{12}{13} \lt -2,5 \gt =\lt -3,\dfrac{70}{13} \gt$
and $|\lt -3,\dfrac{70}{13}\gt|=\sqrt{(-3)^2+(\dfrac{70}{13})^2}=\dfrac{\sqrt{6421}}{13}$
Hence, our final answers are: $\lt -3,\dfrac{70}{13}\gt$ and $\dfrac{\sqrt{6421}}{13}$
