Let the plane P: 8 x+α₁ y+α₂ z+12=0 be parallel to the line L: (x+2)/2=(y-3)/3=(z+4)/5. If the intercept of P on the y -axis is 1, then the distance between P and L is:

Three Dimensional Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 31 Jan, Evening shift · Q2454

JEE Main 202331 Jan, Evening shiftMathematicsMediumThree Dimensional Geometry249× since 2002

Let the plane

\mathrm{P}: 8 x+\alpha_{1} y+\alpha_{2} z+12=0

be parallel to the line

\mathrm{L}: \frac{x+2}{2}=\frac{y-3}{3}=\frac{z+4}{5}

. If the intercept of

\mathrm{P}

on the

y

-axis is 1 , then the distance between

\mathrm{P}

and

\mathrm{L}

is :