Find the equation of the plane containing the points $(2, 3, - 1), (4, 5, 2), (3, 6, 5)$

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Solution

Now,
$\begin{matrix} a (x - 2) + b (y - 3) + c (z + 1) = 0 2 a + 2 b + 3 c = 0 a + 3 b + 6 c = 0 \frac{a}{12 - 9} = \frac{- b}{12 - 3} = \frac{c}{6 - 2} \frac{a}{3} = \frac{b}{- 9} = \frac{c}{4} \Rightarrow 3 (x - 2) - 9 (y - 3) + 4 (z + 1) = 0 3 x - 9 y + 4 z + 25 = 0 \end{matrix}$

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