Plane Rotation About a Line

A question asking to find the equation of a plane obtained by rotating a given plane about a line of intersection by a specified angle.

jee-main 2022 Q79 View
If the plane $2 x + y - 5 z = 0$ is rotated about its line of intersection with the plane $3 x - y + 4 z - 7 = 0$ by an angle of $\frac { \pi } { 2 }$, then the plane after the rotation passes through the point
(1) $( 2 , - 2,0 )$
(2) $( - 2,2,0 )$
(3) $( 1,0,2 )$
(4) $( - 1,0 , - 2 )$
jee-main 2022 Q79 View
Let the plane $2 x + 3 y + z + 20 = 0$ be rotated through a right angle about its line of intersection with the plane $x - 3 y + 5 z = 8$. If the mirror image of the point $\left( 2 , - \frac { 1 } { 2 } , 2 \right)$ in the rotated plane is $B ( a , b , c )$, then
(1) $\frac { a } { 8 } = \frac { b } { 5 } = \frac { c } { - 4 }$
(2) $\frac { a } { 4 } = \frac { b } { 5 } = \frac { c } { - 2 }$
(3) $\frac { a } { 8 } = \frac { b } { - 5 } = \frac { c } { 4 }$
(4) $\frac { a } { 4 } = \frac { b } { 5 } = \frac { c } { 2 }$