The distance of the point (-1,2,3) from the plane r ·(i-2 j+3 k)=10 parallel to the line of the shortest distance between the lines r=(i-j)+λ(2 i+k) and r=(2 i-j)+μ(i-j+k) is:

Three Dimensional Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 13 Apr, Morning shift · Q2466

JEE Main 202313 Apr, Morning shiftMathematicsHardThree Dimensional Geometry249× since 2002

The distance of the point

(-1,2,3)

from the plane

\vec{r} \cdot(\hat{i}-2 \hat{j}+3 \hat{k})=10

parallel to the line of the shortest distance between the lines

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

and

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

is :