Let the system of linear equations – x + 2y - 9z = 7 - x + 3y + 7z...

Given,

System of linear equation,

$– x + 2y - 9z = 7 . . . . . . . \left(i\right)</p><p>$– x + 3y + 7z = 9 . . . . . . . \left(ii\right)$</p><p>$– 2x + y + 5z = 8 . . . . . . \left(iii\right)

$– 3x + y + 13z = \lambda . . . . . . \left(iv\right)$

Now solving, equations \left(i\right), \left(ii\right) \text{$and$} \left(iii\right)$we get,</p><p>$x = – 3, y = 2, z = 0$</p><p>Now substituting in equation \left(iv\right)$ we get,

$3 \times 3 + 2 = \lambda$

$⇒ \lambda = 11$

Now finding the distance of Point \left(– 3, 2, 0\right)$from the plane$2x - 2y + z = 11$we get,</p><p>$d = \left|\dfrac{- 6 - 4 - 11}{\sqrt{{2}^{2} + {2}^{2} + 1}}\right| = \dfrac{21}{3} = 7