a,
$\vec{AB}(4+1; 2-3)=(5;-1)$
$\vec{AC}(3+1; 5-3)=(4;2)$
Vì $\dfrac{5}{4}\ne \dfrac{-1}{2}$
nên $\vec{AB}\ne k\vec{AC}$
Vậy A, B, C không thẳng hàng.
b,
$\vec{BC}=(3-4; 5-2)=(-1;3)$
$\Rightarrow -3\vec{BC}=(3; -9)$
$\Rightarrow D(3-1; -9+3)=(2;-6)$
c,
$O(0;0)$ là trọng tâm $\Delta ABE$.
$\Rightarrow \dfrac{-1+4+x_E}{3}=\dfrac{3+2+y_E}{3}=0$
$\Rightarrow x_E=-3; y_E=-5$
Vậy $E(-3;-5)$
