jee-main 2022 Q68

jee-main · India · session2_26jul_shift1 Simultaneous equations

If the system of linear equations $8 x + y + 4 z = - 2$ $x + y + z = 0$ $\lambda x - 3 y = \mu$ has infinitely many solutions, then the distance of the point $\left( \lambda , \mu , - \frac { 1 } { 2 } \right)$ from the plane $8 x + y + 4 z + 2 = 0$ is:
(1) $3 \sqrt { 5 }$
(2) 4
(3) $\frac { 26 } { 9 }$
(4) $\frac { 10 } { 3 }$

If the system of linear equations\\
$8 x + y + 4 z = - 2$\\
$x + y + z = 0$\\
$\lambda x - 3 y = \mu$\\
has infinitely many solutions, then the distance of the point $\left( \lambda , \mu , - \frac { 1 } { 2 } \right)$ from the plane $8 x + y + 4 z + 2 = 0$ is:\\
(1) $3 \sqrt { 5 }$\\
(2) 4\\
(3) $\frac { 26 } { 9 }$\\
(4) $\frac { 10 } { 3 }$

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