Let the plane P: 4 x-y+z=10 be rotated by an angle (π)/2 about its line of intersection with the plane x+y-z=4. If α is the distance of the point (2,3,-4) from the new position of the plane P, then 35 α is equal to:

Three Dimensional Geometry: JEE Main 2023 Mathematics question

JEE Main 2023 · 12 Apr, Morning shift · Q2467

JEE Main 202312 Apr, Morning shiftMathematicsMediumThree Dimensional Geometry249× since 2002

Let the plane P:

4 x-y+z=10

be rotated by an angle

\frac{\pi}{2}

about its line of intersection with the plane

x+y-z=4

. If

\alpha

is the distance of the point

(2,3,-4)

from the new position of the plane

\mathrm{P}

, then

35 \alpha

is equal to :