If the system of linear equations. … … … has infinitely many solutions, then the distance of the point … from the plane … is :

Option D. …\Delta = \left| {\matrix{ 8 & 1 & 4 \cr 1 & 1 & 1 \cr \lambda & { - 3} & 0 \cr

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Matrices and Determinants

JEE Main 2022 · 26 Jul, Morning shift · Q4613

MathematicsMedium244×since 2002Q4613

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 :