Let P be the foot of the perpendicular from the point (1,2,2) on the line L: (x-1)/1=(y+1)/(-1)=(z-2)/2. Let the line r=(-i+j-2k)+λ(i-j+k), λ R, intersect the line L at Q. Then 2(PQ)² is equal to:

Three Dimensional Geometry: JEE Main 2025 Mathematics question

JEE Main 2025 · January, Unspecified (session-level dataset) · Q129

JEE Main 2025January, Unspecified (session-level dataset)MathematicsMediumThree Dimensional Geometry249× since 2002

Let

P

be the foot of the perpendicular from the point

(1,2,2)

on the line

L: \frac{x-1}{1}=\frac{y+1}{-1}=\frac{z-2}{2}

. Let the line

\vec{r}=(-\hat{i}+\hat{j}-2\hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k})

\lambda \in \mathbb{R}

, intersect the line

L

Q

. Then

2(PQ)^2

is equal to: