Answer
$\left(-\dfrac{28\sqrt{74}}{74},\dfrac{20\sqrt{74}}{74}\right)$
$\left(\dfrac{28\sqrt{74}}{74},-\dfrac{20\sqrt{74}}{74}\right)$
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 $\overrightarrow{QP}$:
$\overrightarrow{u}=\dfrac{\overrightarrow{QP}}{|\overrightarrow{QP}|}=\dfrac{(-4-3,1-(-4))}{\sqrt{(-4-3)^2+[1-(-4)]^2}}=\dfrac{(-7,5)}{\sqrt{74}}=\left(-\dfrac{7}{\sqrt{74}},\dfrac{5}{\sqrt{74}}\right)=\left(-\dfrac{7\sqrt{74}}{74},\dfrac{5\sqrt{74}}{74}\right)$
Two vectors parallel to $\overrightarrow{QP}$ of length 4 are:
$4\overrightarrow{u}=4\left(-\dfrac{7\sqrt{74}}{74},\dfrac{5\sqrt{74}}{74}\right)=\left(-\dfrac{28\sqrt{74}}{74},\dfrac{20\sqrt{74}}{74}\right)$
$-4\overrightarrow{u}=-4\left(-\dfrac{7\sqrt{74}}{74},\dfrac{5\sqrt{74}}{74}\right)=\left(\dfrac{28\sqrt{74}}{74},-\dfrac{20\sqrt{74}}{74}\right)$
