Let the plane P contain the line 2 x+y-z-3=0=5 x-3 y+4 z+9 and be parallel to the line (x+2)/2=(3-y)/(-4)=(z-7)/5. Then the distance of the point A(8,-1,-19) from the plane P measured parallel to the line x/(-3)=(y-5)/4=(2-z)/(-12) is equal to _ _ _ _ _ _ _.

Three Dimensional Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 15 Apr, Morning shift · Q24

JEE Main 202315 Apr, Morning shiftMathematicsMediumThree Dimensional Geometry249× since 2002

Let the plane

P

contain the line

2 x+y-z-3=0=5 x-3 y+4 z+9

and be parallel to the line

\frac{x+2}{2}=\frac{3-y}{-4}=\frac{z-7}{5}

. Then the distance of the point

\mathrm{A}(8,-1,-19)

from the plane

\mathrm{P}

measured parallel to the line

\frac{x}{-3}=\frac{y-5}{4}=\frac{2-z}{-12}

is equal to ______________.

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