If the system of linear equations. $8x + y + 4z = - 2$ $x + y + z = 0$ $\lambda x - 3y = \mu $ has infinitely many solutions, then the distance of the point $\left( {\lambda ,\mu , - {1 \over 2}} \right)$ from the plane $8x + y + 4z + 2 = 0$ is :

Question

If the system of linear equations.

$8x + y + 4z = - 2$

$x + y + z = 0$

$\lambda x - 3y = \mu $

has infinitely many solutions, then the distance of the point $\left( {\lambda ,\mu , - {1 \over 2}} \right)$ from the plane $8x + y + 4z + 2 = 0$ is :

$3\sqrt 5 $

${{26} \over 9}$

${{10} \over 3}$

Solution

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