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

Matrices and Determinants: JEE Main 2022 Mathematics question

JEE Main 2022 · 26 Jul, Morning shift · Q4613

JEE Main 202226 Jul, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

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 :