Let u → = 2 i ^ + j ^ and v → = 3   i ^ - 5   j ^ . Consider three points P ,   Q…

Given that:  $\overrightarrow{u}=2\hat{i}+\hat{j}$ and $\overrightarrow{v}=3 \hat{i}-5 \hat{j}\Rightarrow u(2,1) \& v(3,-5)$

Three points $P(\frac{5}{2},-2), Q(\frac{7}{3},-1)$ and $R(\frac{9}{4},0)$

Line passing through $u \text{and} v$: 

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

$y-1=\frac{-5-1}{3-2}(x-2)$

$y-1=-6x+12$

$6x+y=13$

Put $P(\frac{5}{2},-2), Q(\frac{7}{3},-1) \& R(\frac{9}{4},0)$

$P: 15-2-=13$

$Q: 14-1=13$

$R: \frac{27}{4}+0\ne 13$

$P,Q$satisfy the line joining $\overrightarrow{u} \& \overrightarrow{v}.$