A plane P contains the line of intersection of the plane r ·(i+j+k)=6 and r ·(2 i+3 j+4 k)=-5. If P passes through the point (0,2,-2), then the square of distance of the point (12,12,18) from the plane P is:

Three Dimensional Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 6 Apr, Evening shift · Q2616

JEE Main 20236 Apr, Evening shiftMathematicsMediumThree Dimensional Geometry249× since 2002

A plane P contains the line of intersection of the plane

\vec{r} \cdot(\hat{i}+\hat{j}+\hat{k})=6

and

\vec{r} \cdot(2 \hat{i}+3 \hat{j}+4 \hat{k})=-5

. If

\mathrm{P}

passes through the point

(0,2,-2)

, then the square of distance of the point

(12,12,18)

from the plane

\mathrm{P}

is :