determine o valor de a para que os pontos A(2,1), B(a + 1,2) e C(-3, -1) estejam alinhados :
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Se os pontos estão alinhados, devemos ter:
![\left[\begin{array}{ccc}2&1&2\\a+1&2&1\\-3&-1&1\end{array}\right] = 2(3) -1(a +4)+1(5-a) = 7-2a\\\\\\
fazendo -2a +7 = 0, temos\\\\
-2a+ 7 = 0 \Rightarrow a = \frac{-7}{-2} \iff a = \frac{7}{2}](https://tex.z-dn.net/?f=++%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D2%26amp%3B1%26amp%3B2%5C%5Ca%2B1%26amp%3B2%26amp%3B1%5C%5C-3%26amp%3B-1%26amp%3B1%5Cend%7Barray%7D%5Cright%5D++%3D+2%283%29+-1%28a+%2B4%29%2B1%285-a%29+%3D+7-2a%5C%5C%5C%5C%5C%5C%0Afazendo+-2a+%2B7+%3D+0%2C+temos%5C%5C%5C%5C%0A-2a%2B+7+%3D+0+%5CRightarrow+a+%3D++%5Cfrac%7B-7%7D%7B-2%7D+%5Ciff+a+%3D++%5Cfrac%7B7%7D%7B2%7D+ "\left[\begin{array}{ccc}2&1&2\\a+1&2&1\\-3&-1&1\end{array}\right] = 2(3) -1(a +4)+1(5-a) = 7-2a\\\\\\
fazendo -2a +7 = 0, temos\\\\
-2a+ 7 = 0 \Rightarrow a = \frac{-7}{-2} \iff a = \frac{7}{2}")
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