1. Tardigrade
  2. Question
  3. Mathematics
  4. If the system of linear equations. 8 x+y+4 z=-2 x+y+z=0 λ x-3 y=μ has infinitely many solutions, then the distance of the point (λ, μ,-(1/2)) from the plane 8 x + y +4 z +2=0 is :

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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 :

JEE MainJEE Main 2022Determinants

Solution:

$D = \begin{vmatrix} 8 & 1 & 4 \\1 & 1 & 1 \\\lambda & -3 & 0\end{vmatrix}=0 \Rightarrow \lambda=4$
Also $D _1= D _2= D _3=0$
So $\mu=-2$
Point $\left(4,-2,-\frac{1}{2}\right)$
Distance from plane $=\frac{10}{3}$