Answer
$|\overrightarrow{w}-\overrightarrow{u}|>|\overrightarrow{u}-\overrightarrow{v}|$
Work Step by Step
We are given:
$u=(3,-4)$
$v=(1,1)$
$w=(-1,0)$
Determine the magnitude of $\overrightarrow{u}-\overrightarrow{v}$:
$|\overrightarrow{u}-\overrightarrow{v}|=|(3,-4)-(1,1)|=|(3-1,-4-1)|=|(2,-5)|=\sqrt{2^2+(-5)^2}=2\sqrt{29}$
Determine the magnitude of $\overrightarrow{w}-\overrightarrow{u}$:
$|\overrightarrow{w}-\overrightarrow{u}|=|(-1,0)-(3,-4)|=|(-1-3,0-(-4)|=|(-4,4)|=\sqrt{(-4)^2+4^2}=\sqrt{32}$
As $\sqrt{32}>\sqrt{29}$, we have:
$|\overrightarrow{w}-\overrightarrow{u}|>|\overrightarrow{u}-\overrightarrow{v}|$
