Answer
$\left(-\dfrac{24\sqrt{61}}{61},-\dfrac{20\sqrt{61}}{61}\right)$
$\left(\dfrac{24\sqrt{61}}{61},\dfrac{20\sqrt{61}}{61}\right)$
Work Step by Step
We are given the points:
$P(-4,1)$
$Q(3,-4)$
$R(2,6)$
Find the unit vector $\overrightarrow{u}$ with the same direction as $\overrightarrow{RP}$:
$\overrightarrow{u}=\dfrac{\overrightarrow{RP}}{|\overrightarrow{RP}|}=\dfrac{(-4-2,1-6)}{\sqrt{(-4-2)^2+(1-6)^2}}=\dfrac{(-6,-5)}{\sqrt{61}}=\left(-\dfrac{6}{\sqrt{61}},-\dfrac{5}{\sqrt{61}}\right)=\left(-\dfrac{6\sqrt{61}}{61},-\dfrac{5\sqrt{61}}{61}\right)$
Two unit vectors parallel to $\overrightarrow{RP}$ are:
$4\overrightarrow{u}=4\left(-\dfrac{6\sqrt{61}}{61},-\dfrac{5\sqrt{61}}{61}\right)=\left(-\dfrac{24\sqrt{61}}{61},-\dfrac{20\sqrt{61}}{61}\right)$
$-4\overrightarrow{u}=-4\left(-\dfrac{6\sqrt{61}}{61},-\dfrac{5\sqrt{61}}{61}\right)=\left(\dfrac{24\sqrt{61}}{61},\dfrac{20\sqrt{61}}{61}\right)$
