Answer
$2\overrightarrow{u}$ has a greater magnitude
Work Step by Step
We are given:
$u=(3,-4)$
$v=(1,1)$
$w=(-1,0)$
Determine the magnitude of $2\overrightarrow{u}$:
$2|\overrightarrow{u}|=2|(3,-4)|=2\sqrt{3^2+(-4)^2}=2\sqrt{25}=2(5)=10$
Determine the magnitude of $7\overrightarrow{v}$:
$7|\overrightarrow{v}|=7|(1,1)|=7\sqrt{1^2+1^2}=7\sqrt 2\approx 9.9$
As $10>9.9$, we have:
$|2\overrightarrow{u}|>|7\overrightarrow{v}|$
