Question

In xOy se dau punctele A(1,4) , B(2,1) , C(3,a) . Determinati numarul real a , astfel incat punctele A,B si C sa fie coliniare.

Answer 1

$\left|\begin{array}{ccc}1&4&1\\2&1&1\\3&a&1\end{array}\right|\stackrel{L1-L2}=\left|\begin{array}{ccc}1&4&1\\-1&3&0\\3&a&1\end{array}\right|\stackrel{L1-L3}=\left|\begin{array}{ccc}1&4&1\\-1&3&0\\-2&4-a&0\end{array}\right|=\\\\=(-1)^{1+3}\cdot 1\cdot\left|\begin{array}{cc}-1&3\\-2&4-a\end{array}\right|=a-4+6=0,\;deci\;a=-2.$