QJEEM22Ma44f8: JEE Main 2022 Mathematics - Class 12 JEEM22Ma44f8 Solution: If the system of linear equations. has infinitely many…

$$\mathrm{\Delta }=\left|\begin{array}{ccc}8& 1& 4\\ 1& 1& 1\\ \lambda & -3& 0\end{array}\right|$$

$= 8(3) - 1( - \lambda ) + 4( - 3 - \lambda )$

$= 24 + \lambda - 12 - 4\lambda$

$= 12 - 3\lambda$

So for $\lambda = 4$ , it is having infinitely many solutions.

$${\mathrm{\Delta }}_x=\left|\begin{array}{ccc}-2& 1& 4\\ 0& 1& 1\\ \mu & -3& 0\end{array}\right|$$

$= - 2(3) - 1( - \mu )+4( - \mu )$

$= - 6 - 3\mu = 0$

For $\mu = - 2$

Distance of $(4, - 2,{{ - 1} \over 2})$ from $8x + y + 4z + 2 = 0$

$= {{32 - 2 - 2 + 2} \over {\sqrt {64 + 1 + 16} }} = {{10} \over 3}$ units