Problems from General equation of a plane

Determine the general equation of a plane that goes through point $A = (1, 0, 3)$ and has as director vectors $\vec{u} = (- 1, 3, 2)$ and $\vec{v} = (2, 1, 0)$ .

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Development:

If we equate the following determinant to $0$ , using the point and the director vectors, we obtain the general equation: $| \begin{matrix} x - 1 & - 1 & 2 \\ y & 3 & 1 \\ z - 3 & 2 & 0 \end{matrix} | = - (z - 3) + 4 y - 6 (z - 3) - 2 (x - 1) = - 2 x + 4 y - 7 z + 23 = 0$

Solution:

Therefore the general equation is $- 2 x + 4 y - 7 z + 23 = 0$

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