Question

let u = \overrightarrow{xy} where x(-4, 6) and y(8, 3). what is |2u|?
6\sqrt{17}
18
3\sqrt{17}
612

Explanation:

Step1: Find vector $\vec{u}$ components

If $X(-4,6)$ and $Y(8,3)$, then $\vec{u}=\overrightarrow{XY}=(8 - (-4),3 - 6)=(12,-3)$.

Step2: Find vector $2\vec{u}$

$2\vec{u}=2(12,-3)=(2\times12,2\times(-3))=(24,-6)$.

Step3: Calculate the magnitude of $2\vec{u}$

The magnitude of a vector $\vec{v}=(a,b)$ is $|\vec{v}|=\sqrt{a^{2}+b^{2}}$. For $2\vec{u}=(24,-6)$, $|2\vec{u}|=\sqrt{24^{2}+(-6)^{2}}=\sqrt{576 + 36}=\sqrt{612}=\sqrt{36\times17}=6\sqrt{17}$.

Answer:

A. $6\sqrt{17}$