Question

Find the equation of the plane passing through the following points.

 (−5, 0, −6), (−3, 10, −9) and (−2, 6, −6)

Answer 1

The equation of the plane passing through points (−5, 0, −6), (−3, 10, −9) and (−2, 6, −6) is given by 

\[\begin{vmatrix}x + 5 & y - 0 & z + 6 \\ - 3 + 5 & 10 - 0 & - 9 + 6 \\ - 2 + 5 & 6 - 0 & - 6 + 6\end{vmatrix} = 0\]

\[\]

\[ \Rightarrow \begin{vmatrix}x + 5 & y & z + 6 \\ 2 & 10 & - 3 \\ 3 & 6 & 0\end{vmatrix} = 0\]

\[\]

\[ \Rightarrow 18 \left( x + 5 \right) - 9y - 18 \left( z + 6 \right) = 0\]

\[ \Rightarrow 2 \left( x + 5 \right) - y - 2 \left( z + 6 \right) = 0\]

\[ \Rightarrow 2x + 10 - y - 2z - 12 = 0\]

\[ \Rightarrow 2x - y - 2z - 2 = 0\]

\[\]