Find the equation of the plane containing the line $2 x - 5 y + 2 z = 6, 2 x + 3 y - z = 5$ and parallel to the line $\frac{x}{1} = \frac{- y}{6} = \frac{z}{7}$

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Solution

$2 x - 5 y = 6$
$2 x + - 3 y = - 5 - - --------- -$
$- 8 y = 1 \Rightarrow y = - 1 / 8$
$2 x = 6 + 5 y = 6 \frac{- 5}{8} = \frac{43}{8}$
$x = \frac{43}{16}$
$\to a = (\frac{43}{18})^i - (\frac{1}{8})^i + 0.^k$

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