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प्रश्न
Find the equation of the plane passing through the following points.
(2, 3, 4), (−3, 5, 1) and (4, −1, 2)
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उत्तर
The equation of the plane passing through points (2, 3, 4), (−3, 5, 1) and (4, −1, 2) is given by
\[\begin{vmatrix}x - 2 & y - 3 & z - 4 \\ - 3 - 2 & 5 - 3 & 1 - 4 \\ 4 - 2 & - 1 - 3 & 2 - 4\end{vmatrix} = 0\]
\[\]
\[ \Rightarrow \begin{vmatrix}x - 2 & y - 3 & z - 4 \\ - 5 & 2 & - 3 \\ 2 & - 4 & - 2\end{vmatrix} = 0\]
\[\]
\[ \Rightarrow - 16 \left( x - 2 \right) - 16 \left( y - 3 \right) + 16 \left( z - 4 \right) = 0\]
\[ \Rightarrow \left( x - 2 \right) + \left( y - 3 \right) - \left( z - 4 \right) = 0\]
\[ \Rightarrow x + y - z = 1\]
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